Reduced diameter single mode optical fibers with high mechanical reliability

ABSTRACT

The optical fibers disclosed is a single mode optical fiber comprising a core region and a cladding region surrounding and directly adjacent to the core region. The core region can have a radius r 1  in a range from 3 μm to 7 μm and a relative refractive index profile Δ 1  having a maximum relative refractive index Δ 1max  in the range from 0.25% to 0.50%. The cladding region can include a first outer cladding region and a second outer cladding region surrounding and directly adjacent to the first outer cladding region. The first outer cladding region can have a radius r 4a . The second outer cladding region can have a radius r 4b  less than or equal to 45 μm and comprising silica based glass doped with titania.

This application claims priority under 35 USC § 119(e) from U.S.Provisional Patent Application Ser. No. 63/023,420 filed on May 12, 2020which is incorporated by reference herein in its entirety.

FIELD

The present disclosure relates to optical fibers and in particularrelates to reduced diameter single mode optical fibers with highmechanical reliability.

BACKGROUND

There is an increasing demand for optical fiber transmissioncapacity—driven by the rapid growth of internet traffic. The need forgreater bandwidth and higher data transmission rates has motivatedefforts to develop next-generation platforms for information storage anddelivery. It is widely believed that optical information systems canprovide superior performance as compared to present-day,microelectronics-based systems.

Data centers commonly employ vertical-cavity surface-emitting lasers(VCSEL) optical information transmission. However, chromatic dispersionis a limiting factor for high data rates and/or long-reach links becauseof the large transceiver linewidth associated with VCSELs. An example ofso affected VCSELs are those that, for example, transmit over singlemode fibers using a wavelength of approximately 850 nm. Integratedoptical systems based on silicon photonics or long wavelength VCSELs area leading replacement technology for microelectronic systems. Siliconphotonics may be interfaced with standard CMOS technologies and WDM(wavelength division multiplexing) to provide numerous functions—forexample, convert electrical signals to optical signals, transmit opticalsignals, and reconvert optical signals to electrical signals.

To increase the transmission capacity, WDM and spatial divisionmultiplexing (SDM) have been used to increase the number of transmissionchannels. Advanced modulation formats have been developed to increasethe data rate per channel. However, the number of channels and thechannel data rate are nearly at the practical limits and increasing thenumber of fibers is unavoidable. A method to overcome this bottleneck isto upscale the hardware (e.g., more fibers). However, limited spaceavailability at data centers and increased costs discourage suchimplementations.

Optical fibers with small cladding and coating diameters are attractivefor reducing the size and cost of fibers and increasing the bandwidthdensity of optical interconnects. It is also desirable to use thinnerlayers as primary and/or secondary coatings in reduced-cladding-diameterfibers. However, the smaller cladding diameter increases themicrobending sensitivity, and thinner coating diameters furthercompromise the microbend performance as well as the protective functionof the coatings. As a result, commercially availablereduced-cladding-diameter fibers tend to have small mode fielddiameters, high numerical apertures, and/or high cutoff wavelengths toreduce bend sensitivity at long wavelengths, for example, aboveapproximately 1530 nm. And conventional coating solutions may not besufficient to achieve low attenuation and low bend losses.

It is therefore desirable to design a single mode optical fiber havingreduced cladding and coating diameters, low attenuation, low bendlosses, a G.657-compliant mode field diameter, and a low cutoffwavelength. Smaller cladding diameters also allow the fiber to bedeployed in tight bends. There are applications that require evensmaller bend radii for the same arc length or multiple bend conditionsat the same bend radius. For such bend requirements, the use of atitanium-doped cladding increases reliability of the fiber.

BRIEF SUMMARY

The present disclosure is directed to optical fiber cables having hightransmission capacity, low transmission loss, low cutoff wavelength, lowmicrobending loss, high puncture resistance, and high overall mechanicalreliability.

Aspect 1 of the description discloses: A single mode optical fiber,comprising: a core region, the core region having a radius r₁ in a rangefrom 3 μm to 7 μm and a relative refractive index profile Δ₁ having amaximum relative refractive index Δ_(1max) in the range from 0.25% to0.50%; and a cladding region surrounding and directly adjacent to thecore region, the cladding region including a first outer cladding regionand a second outer cladding region surrounding and directly adjacent tothe first outer cladding region, the first outer cladding region havinga radius r_(4a), the second outer cladding region having a radius r_(4b)less than or equal to 45 μm and comprising silica based glass doped withtitania.

Aspect 2 of the description discloses: The single mode optical fiber ofAspect 1, wherein the radius r₁ is in a range from 3.5 μm to 6.0 μm.

Aspect 3 of the description discloses: The single mode optical fiber ofAspect 1 or 2, wherein the relative refractive index profile Δ₁ is agraded-index relative refractive index profile.

Aspect 4 of the description discloses: The single mode optical fiber ofAspect 1 or 2, wherein the relative refractive index profile Δ₁ is anα-profile with a value of a greater than 5.

Aspect 5 of the description discloses: The single mode optical fiber ofAspect 1 or 2, wherein the relative refractive index profile Δ₁ is astep-index relative refractive index profile.

Aspect 6 of the description discloses: The single mode optical fiber ofany of Aspects 1-5, wherein the maximum relative refractive indexΔ_(1max) is in the range from 0.30% to 0.45%;

Aspect 7 of the description discloses: The single mode optical fiber ofany of Aspects 1-6, wherein the cladding region includes an innercladding region surrounding and directly adjacent to the core region,the inner cladding region having a radius r₂, a thickness (r₂−r₁) in arange from 2 μm to 8 μm and a relative refractive index Δ₂ in a rangefrom −0.10% to 0.10%.

Aspect 8 of the description discloses: The single mode optical fiber ofAspect 7, wherein the cladding region further comprises adepressed-index cladding region surrounding and directly adjacent to theinner cladding region, the depressed-index cladding region having aradius r₃, a thickness (r₃−r₂) in a range from 3 μm to 10 μm, and arelative refractive index Δ₃ in a range from −0.70% to −0.20%.

Aspect 9 of the description discloses: The single mode optical fiber ofAspect 8, wherein the thickness (r₃−r₂) in a range from 4 μm to 8 μm.

Aspect 10 of the description discloses: The single mode optical fiber ofAspect 8 or 9, wherein the depressed-index cladding region has a has atrench volume V₃ in a range from 30% %Δ-μm² to 80%Δ-μm².

Aspect 11 of the description discloses: The single mode optical fiber ofany of Aspects 8-10, wherein the first outer cladding region surroundsand is directly adjacent to the depressed-index cladding region.

Aspect 12 of the description discloses: The single mode optical fiber ofany of Aspects 1-11, wherein the first outer cladding region has arelative refractive index Δ_(4a) that is in the range from −0.10% to0.10% and the second outer cladding region has a relative refractiveindex Δ_(4b) greater than 0.20%.

Aspect 13 of the description discloses: The single mode optical fiber ofany of Aspects 1-12, wherein the second outer cladding region has atitania concentration in a range from 5 wt % to 20 wt %.

Aspect 14 of the description discloses: The single mode optical fiber ofany of Aspects 1-13, wherein the radius r_(4b) is less than or equal to40 μm.

Aspect 15 of the description discloses: The single mode optical fiber ofany of Aspects 1-14, wherein the second outer cladding region has athickness (r_(4b)−r_(4a)) in a range from 2 μm to 30 μm.

Aspect 16 of the description discloses: The single mode optical fiber ofany of Aspects 1-15, further comprising: a primary coating surroundingand directly adjacent to the second outer cladding region, the primarycoating having a radius r₅ less than or equal to 65 μm, a springconstant χ_(p) less than 1.2 MPa, an in situ modulus in the range from0.05 MPa to 0.30 MPa, and a thickness (r₅−r₄) less than 30 μm.

Aspect 17 of the description discloses: The single mode optical fiber ofany of Aspects 1-16, wherein the radius r₅ is less than or equal to 60μm.

Aspect 18 of the description discloses: The single mode optical fiber ofany of Aspects 1-16, wherein the radius r₅ is less than or equal to 55μm.

Aspect 19 of the description discloses: The single mode optical fiber ofany of Aspects 1-18, wherein the spring constant χ_(p) less than 0.8MPa.

Aspect 20 of the description discloses: The single mode optical fiber ofany of Aspects 1-19, wherein the thickness (r₅−r₄) is less than 20 μm.

Aspect 21 of the description discloses: The single mode optical fiber ofany of Aspects 1-20, wherein the thickness (r₅−r₄) is greater than 10μm.

Aspect 22 of the description discloses: The single mode optical fiber ofany of Aspects 1-21, wherein the primary coating is a cured product of acoating composition comprising: a radiation-curable monomer; an adhesionpromoter, the adhesion promoter comprising an alkoxysilane compound or amercapto-functional silane compound; and an oligomer, the oligomercomprising: a polyether urethane acrylate compound having the molecularformula:

wherein R₁, R₂ and R₃ are independently selected from linear alkylenegroups, branched alkylene groups, or cyclic alkylene groups; y is 1, 2,3, or 4; and x is between 40 and 100; and a di-adduct compound havingthe molecular formula:

wherein the di-adduct compound is present in an amount of at least 1.0wt % in the oligomer.

Aspect 23 of the description discloses: The single mode optical fiber ofAspect 22, wherein the oligomer is the cured product of a reactionbetween: a diisocyanate compound; a hydroxy (meth)acrylate compound; anda polyol compound, said polyol compound having unsaturation less than0.1 meq/g; wherein said diisocyanate compound, said hydroxy(meth)acrylate compound and said polyol compound are reacted in molarratios n:m:p, respectively, wherein n is in the range from 3.0 to 5.0, mis within ±15% of 2n−4, and p is 2.

Aspect 24 of the description discloses: The single mode optical fiber ofany of Aspects 16-23, further comprising: a secondary coatingsurrounding and directly adjacent to the primary coating, the secondarycoating having a radius r₆ less than or equal to 85 μm, a Young'smodulus greater than 1600 MPa and a thickness (r₆−r₅) less than 30 μm.

Aspect 25 of the description discloses: The single mode optical fiber ofAspect 24, wherein the radius r₆ is less than or equal to 80 μm.

Aspect 26 of the description discloses: The single mode optical fiber ofAspect 24, wherein the radius r₆ is less than or equal to 75 μm.

Aspect 27 of the description discloses: The single mode optical fiber ofany of Aspects 24-26, wherein the thickness (r₆−r₅) is less than 20 μm.

Aspect 28 of the description discloses: The single mode optical fiber ofany of Aspects 24-27, wherein the thickness (r₆−r₅) is greater than 10μm.

Aspect 29 of the description discloses: The single mode optical fiber ofany of Aspects 24-28, wherein the secondary coating has a Young'smodulus greater than 2000 MPa.

Aspect 30 of the description discloses: The single mode optical fiber ofany of Aspects 24-29, wherein the secondary coating is the cured productof a composition comprising: an alkoxylated bisphenol-A diacrylatemonomer in an amount greater than 55 wt %, the alkoxylated bisphenol-Adiacrylate monomer having a degree of alkoxylation in the range from 2to 16; and a triacrylate monomer in an amount in the range from 2.0 wt %to 25 wt %, the triacrylate monomer comprising an alkoxylatedtrimethylolpropane triacrylate monomer having a degree of alkoxylationin the range from 2 to 16 or a tris[(acryloyloxy)alkyl] isocyanuratemonomer.

Aspect 31 of the description discloses: The single mode optical fiber ofAspect 30, wherein the alkoxylated trimethylolpropane triacrylatemonomer is an ethoxylated trimethylolpropane triacrylate monomer.

Aspect 32 of the description discloses: The single mode optical fiber ofAspect 30 or 31, wherein the tris[(acryloyloxy)alkyl] isocyanuratemonomer is a tris(2-hydroxyethyl) isocyanurate triacrylate monomer.

Aspect 33 of the description discloses: The single mode optical fiber ofany of Aspects 24-32, wherein the secondary coating has a normalizedpuncture load greater than 3.5×10⁻³ g/μm².

Aspect 34 of the description discloses: The single mode optical fiber ofany of Aspects 24-33, wherein a ratio R_(ps) of the thickness (r₅−r₄) ofthe primary coating to the thickness (r₆−r₅) of the secondary coating isin a range from 0.90 to 1.50.

Aspect 35 of the description discloses: The single mode optical fiber ofany of Aspects 24-34, further comprising a tertiary coating surroundingand directly adjacent to the secondary coating, the tertiary coatingcomprising a pigment and having a thickness in the range from 2.0 μm to8.0 μm.

Aspect 36 of the description discloses: The single mode optical fiber ofany of Aspects 1-35, wherein the single mode optical fiber has a fibercutoff wavelength λ_(CF) less than 1310 nm.

Aspect 37 of the description discloses: The single mode optical fiber ofany of Aspects 1-35, wherein the single mode optical fiber has a fibercutoff wavelength λ_(CF) less than 1280 nm.

Aspect 38 of the description discloses: The single mode optical fiber ofany of Aspects 1-37, wherein the single mode optical fiber has a modefield diameter (MFD) greater than 8.2 at 1310 nm.

Aspect 39 of the description discloses: The single mode optical fiber ofany of Aspects 1-37, wherein the single mode optical fiber has a modefield diameter (MFD) in a range from 8.6 μm to 9.5 μm at 1310 nm.

Aspect 40 of the description discloses: The single mode optical fiber ofany of Aspects 1-39, wherein the single mode optical fiber has a bendloss at 1550 nm, as determined by a mandrel wrap test using a mandrelwith a diameter of 10 mm, less than 1.0 dB/turn.

Aspect 41 of the description discloses: The single mode optical fiber ofany of Aspects 1-39, wherein the single mode optical fiber has a bendloss at 1550 nm, as determined by a mandrel wrap test using a mandrelwith a diameter of 10 mm, less than 0.5 dB/turn.

Aspect 42 of the description discloses: The single mode optical fiber ofany of Aspects 1-39, wherein the single mode optical fiber has a bendloss at 1550 nm, as determined by a mandrel wrap test using a mandrelwith a diameter of 15 mm, less than 0.25 dB/turn.

Aspect 43 of the description discloses: The single mode optical fiber ofany of Aspects 1-39, wherein the single mode optical fiber has a bendloss at 1550 nm, as determined by a mandrel wrap test using a mandrelwith a diameter of 20 mm, less than 0.15 dB/turn.

Aspect 44 of the description discloses: The single mode optical fiber ofany of Aspects 1-39, wherein the single mode optical fiber has anattenuation, as determined by a wire-mesh-covered-drum test, less than1.0 dB/km at 1550 nm.

Aspect 45 of the description discloses: The single mode optical fiber ofany of Aspects 1-39, wherein the single mode optical fiber has anattenuation, as determined by a wire-mesh-covered-drum test, less than0.5 dB/km at 1550 nm.

Aspect 46 of the description discloses: The single mode optical fiber ofany of Aspects 1-45, wherein the single mode optical fiber has a zerodispersion wavelength λ₀ in a range from 1300 nm to 1324 nm.

Additional features and advantages are set forth in the DetailedDescription that follows, and in part will be apparent to those skilledin the art from the description or recognized by practicing theembodiments as described in the written description and claims hereof,as well as the appended drawings. It is to be understood that both theforegoing general description and the following Detailed Description aremerely exemplary, and are intended to provide an overview or frameworkto understand the nature and character of the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying figures, which are incorporated herein, form part ofthe specification and illustrate embodiments of the present disclosure.Together with the description, the figures further serve to explain theprinciples of and to enable a person skilled in the relevant art(s) tomake and use the disclosed embodiments. These figures are intended to beillustrative, not limiting. Although the disclosure is generallydescribed in the context of these embodiments, it should be understoodthat it is not intended to limit the scope of the disclosure to theseparticular embodiments. In the drawings, like reference numbers indicateidentical or functionally similar elements.

FIG. 1 is a side elevated view of a section of an exemplary opticalfiber, according to some embodiments.

FIG. 2 is a cross-sectional view of an exemplary optical fiber,according to some embodiments.

FIG. 3 is a schematic view of a representative optical fiber ribbon,according to some embodiments.

FIG. 4 is a schematic view of a representative optical fiber cable,according to some embodiments.

FIG. 5 shows an optical fiber coupled to a Si photonic waveguide througha ferrule connector with a curved hole for supporting a section of theoptical fiber.

FIG. 6 shows the relationship between minimum bend radius and fibercladding diameter.

FIGS. 7A through 7E are exemplary relative refractive index profiles ofan optical fiber, according to some embodiments.

FIGS. 8A through 8I are exemplary axial stress profiles of an opticalfiber, according to some embodiments.

FIG. 9 shows the dependence of puncture load on cross-sectional area forthree secondary coatings.

FIG. 10 is a schematic diagram of an exemplary optical fiber drawingsystem illustrating fabrication of an optical fiber, according to someembodiments.

DETAILED DESCRIPTION

Embodiments of the present disclosure are described in detail hereinwith reference to embodiments thereof as illustrated in the accompanyingdrawings, in which like reference numerals are used to indicateidentical or functionally similar elements. References to “oneembodiment,” “an embodiment,” “some embodiments,” “in certainembodiments,” etc., indicate that the embodiment described may include aparticular feature, structure, or characteristic, but every embodimentmay not necessarily include the particular feature, structure, orcharacteristic. Moreover, such phrases are not necessarily referring tothe same embodiment. Further, when a particular feature, structure, orcharacteristic is described in connection with an embodiment, it issubmitted that it is within the knowledge of one skilled in the art toaffect such feature, structure, or characteristic in connection withother embodiments whether or not explicitly described.

The following examples are illustrative, but not limiting, of thepresent disclosure. Other suitable modifications and adaptations of thevariety of conditions and parameters normally encountered in the field,and which would be apparent to those skilled in the art, are within thespirit and scope of the disclosure.

Where a range of numerical values is recited herein, comprising upperand lower values, unless otherwise stated in specific circumstances, therange is intended to include the endpoints thereof, and all integers andfractions within the range. It is not intended that the scope of theclaims be limited to the specific values recited when defining a range.Further, when an amount, concentration, or other value or parameter isgiven as a range, one or more preferred ranges or a list of upperpreferable values and lower preferable values, this is to be understoodas specifically disclosing all ranges formed from any pair of any upperrange limit or preferred value and any lower range limit or preferredvalue, regardless of whether such pairs are separately disclosed.Finally, when the term “about” is used in describing a value or anend-point of a range, the disclosure should be understood to include thespecific value or end-point referred to. When a numerical value orend-point of a range does not recite “about,” the numerical value orend-point of a range is intended to include two embodiments: onemodified by “about,” and one not modified by “about.”

As used herein, the term “about” means that amounts, sizes,formulations, parameters, and other quantities and characteristics arenot and need not be exact, but may be approximate and/or larger orsmaller, as desired, reflecting tolerances, conversion factors, roundingoff, measurement error and the like, and other factors known to those ofskill in the art.

As used herein, “comprising” is an open-ended transitional phrase. Alist of elements following the transitional phrase “comprising” is anon-exclusive list, such that elements in addition to those specificallyrecited in the list may also be present.

The term “or,” as used herein, is inclusive; more specifically, thephrase “A or B” means “A, B, or both A and B.” Exclusive “or” isdesignated herein by terms such as “either A or B” and “one of A or B,”for example.

The indefinite articles “a” and “an” to describe an element or componentmeans that one or at least one of these elements or components ispresent. Although these articles are conventionally employed to signifythat the modified noun is a singular noun, as used herein the articles“a” and “an” also include the plural, unless otherwise stated inspecific instances. Similarly, the definite article “the,” as usedherein, also signifies that the modified noun may be singular or plural,again unless otherwise stated in specific instances.

The term “wherein” is used as an open-ended transitional phrase, tointroduce a recitation of a series of characteristics of the structure.

Cartesian coordinates are used in some of the Figures for the sake ofreference and ease of illustration and are not intended to be limitingas to direction or orientation. The z-direction is taken as the axialdirection of the optical fiber.

The term “fiber” as used herein is shorthand for optical fiber.

The coordinate r is a radial coordinate, where r=0 corresponds to thecenterline of the fiber. The term “radius” refers to a value of theradial coordinate. The term “outer radius”, when used in reference to aregion of a fiber, refers to the largest radial coordinate included inthe region. The term “diameter”, when used in reference to a region of afiber, refers to twice the outer radius of the region.

The term “core” as used herein is a core region of an optical fiber,representing a cylinder of material, centered at r=0, that runs alongthe optical fiber's length. The core is characterized by its radius ofcross-sectional area corresponding to confinement (e.g. 90%) of opticalintensity in the optical fiber. The core is surrounded by a medium witha lower index of refraction, typically a cladding region. Lighttravelling in the core reflects from the core-cladding boundary due tototal internal reflection, as long as the angle between the light andthe boundary is greater than the critical angle. As a result, theoptical fiber transmits all rays that enter the fiber with asufficiently small angle relative to the optical fiber's axis.

The term “core radius” as used herein is referred to geometric coreradius which is determined from the refractive index profile.

The symbol “μm” is used as shorthand for “micron,” which is amicrometer, i.e., 1×10⁻⁶ meter.

The symbol “nm” is used as shorthand for “nanometer,” which is 1×10⁻⁹meter.

The limits on any ranges cited herein are inclusive and thus to liewithin the range, unless otherwise specified.

The terms “comprising,” and “comprises,” e.g., “A comprises B,” isintended to include as a special case the concept of “consisting,” as in“A consists of B.”

The phrase “bare optical fiber” or “bare fiber” as used herein means anoptical fiber directly drawn from a heated glass source (i.e., a“preform”) and prior to applying a protective coating layer to its outersurface (e.g., prior to the bare optical fiber being coated with apolymeric-based material).

“Refractive index” refers to the refractive index at a wavelength of1550 nm.

The “refractive index profile” is the relationship between refractiveindex or relative refractive index and radius. For relative refractiveindex profiles depicted herein as having step boundaries betweenadjacent core and/or cladding regions, normal variations in processingconditions may preclude obtaining sharp step boundaries at the interfaceof adjacent regions. It is to be understood that although boundaries ofrefractive index profiles may be depicted herein as step changes inrefractive index, the boundaries in practice may be rounded or otherwisedeviate from perfect step function characteristics. It is furtherunderstood that the value of the relative refractive index may vary withradial position within the core region and/or any of the claddingregions. When relative refractive index varies with radial position in aparticular region of the fiber (e.g. core region and/or any of thecladding regions), it is expressed in terms of its actual or approximatefunctional dependence, or its value at a particular position within theregion, or in terms of an average value applicable to the region as awhole. Unless otherwise specified, if the relative refractive index of aregion (e.g. core region and/or any of the cladding regions) isexpressed as a single value or parameter (e.g. Δ or Δ%) applicable tothe region as a whole, it is understood that the relative refractiveindex in the region is constant, or approximately constant, andcorresponds to the single value, or that the single value or parameterrepresents an average value of a non-constant relative refractive indexdependence with radial position in the region. For example, if “i” is aregion of the glass fiber, the parameter Δ_(i) refers to the averagevalue (Δ_(ave)) of relative refractive index in the region as definedbelow, unless otherwise specified. Whether by design or a consequence ofnormal manufacturing variability, the dependence of relative refractiveindex on radial position may be sloped, curved, or otherwisenon-constant.

The average relative refractive index (Δ_(ave)) of a region of the fiberis determined from:

$\Delta_{ave} = {\int_{r_{inner}}^{r_{outer}}\frac{{\Delta(r)}{dr}}{( {r_{outer} - r_{inner}} )}}$where r_(inner) is the inner radius of the region, r_(outer) is theouter radius of the region, and Δ(r) is the relative refractive index ofthe region.

The “relative refractive index” as used herein is defined as:

${{\Delta(r)}\%} = {100\frac{{n^{2}(r)} - n_{cl}^{2}}{2{n^{2}(r)}}}$where n(r) is the refractive index of the fiber at the radial distance rfrom the fiber's centerline AC (r=0) at a wavelength of 1550 nm, unlessotherwise specified, and n_(cl) is a reference refractive indexcorresponding to the refractive index of pure silica, for whichn_(c1)=1.444 at a wavelength of 1550 nm.

In the description that follows, the relative refractive index (alsoreferred herein as the “relative refractive index percent” for short) isrepresented by Δ (or “delta”), Δ% (or “delta %”), or %, all of which canbe used interchangeably, and its values are given in units of percent or%, unless otherwise specified. Relative refractive index is alsoexpressed as Δ(r) or Δ(r) %.

In some embodiments, the bare optical fiber includes a region with arefractive index less than the reference index n_(cl), which means thatthe relative refractive index percent of the region is negative. Inother embodiments, the bare optical fiber includes a region with arefractive index greater than the reference index n_(cl), which meansthat the relative refractive index percent of the region is positive. Insome embodiments, the bare optical fiber includes a region with anegative relative refractive index percent and a region with a positiverelative refractive index percent. The minimum relative refractive indexof a region corresponds to the point in the region at which the relativerefractive index is lowest. The maximum relative refractive index of aregion corresponds to the point in the region at which the relativerefractive index is greatest. Depending on the relative refractive indexprofile and on the region, each of the minimum relative refractive indexand the maximum relative refractive index may be positive or negative.

In some embodiments, the term “dopant” refers to a substance thatchanges the relative refractive index of glass relative to pure un-dopedSiO₂. In some embodiments, one or more other substances that are notupdopants may be present in a region of an optical fiber (e.g., thecore) having a positive relative refractive index Δ. That is, in someembodiments, the core includes an updopant and a downdopant and has anet relative refractive index that is positive. In some embodiments, thedopants used to form the core of the optical fiber disclosed hereininclude GeO₂ (germania), Al₂O₃ (alumina), and the like. Dopants thatincrease the relative refractive index of glass relative to pureun-doped SiO₂ are referred to as up-dopants and dopants that decreasethe relative refractive index of glass relative to pure un-doped SiO₂are referred to as down-dopants. Glass that contains an up-dopant issaid to be “up-doped” relative to pure un-doped SiO₂ and glass thatcontains a down-dopant is said to be “down-doped” relative to pureun-doped SiO₂. When the undoped glass is silica glass, updopants includeCl, Br, Ge, Al, P, Ti, Zr, Nb, Ta, and oxides thereof, and downdopantsinclude F and B. When comparing two doped glasses (or two doped regionsof a bare optical fiber), the doped glass (or glass region) having thehigher relative refractive index is said to be up-doped relative to thedoped glass (or glass region) having a lower relative refractive indexand the doped glass (or glass region) having the lower relativerefractive index is said to be down-doped relative to the doped glass(or glass region) having the higher relative refractive index. Glassregions of constant refractive index may be formed by not doping or bydoping at a uniform concentration over the thickness of the region.Regions of variable refractive index are formed through non-uniformspatial distributions of dopants over the thickness of a region and/orthrough incorporation of different dopants in different portions of aregion.

In some embodiments, the relative refractive index of a region is anα-profile defined by a parameter α. The parameter α (also called the“profile parameter” or “alpha parameter”) relates to the relativerefractive Δ(r) of a region through the equation:Δ(r)=Δ₀{1−1[(r−r _(m))/(r ₀ −r _(m))]^(α)}where r_(m) is the point where Δ(r) is the maximum Δ₀, r₀ is the pointat which Δ(r) reaches a minimum value and r is in the range r_(i) tor_(f), where Δ(r) is defined above, r_(i) is the initial point of theα-profile, r_(f) is the final point of the α-profile and α is anexponent that is a real number. In one example, r₀ is the point at whichΔ(r)=0. At low values of α, the α-profile is a graded-index profile. Asthe value of a increases, the α-profile more closely resembles astep-index profile. For purposes of the present disclosure, an α-profilewith α≥10 is regarded as a step-index relative refractive profile and anα-profile with α<10 is regarded as a graded relative refractive indexprofile.

The “trench volume” is denoted by V_(Trench) and is defined asV _(Trench)=|2∫_(T) _(Trench,inner) ^(T) ^(Trench,outer)Δ_(Trench)(r)rdr|where r_(Trench,inner) is the inner radius of the trench region of therefractive index profile, r_(Trench,outer) is the outer radius of thetrench region of the refractive index profile, Δ_(Trench)(r) is therelative refractive index of the trench region of the refractive indexprofile, and r is radial position in the fiber. In one embodiment, thetrench region is an inner cladding region and r_(Trench,inner) is r_(i),r_(Trench,outer) is r₂, and Δ_(Trench) is Δ₂. In another embodiment, thetrench region is a depressed-index cladding region and r_(Trench,inner)is r₂, r_(Trench,outer) is r₃, and Δ_(Trench) is Δ₃. Trench volume isdefined as an absolute value and has a positive value. Trench volume isexpressed herein in units of %Δμm², %Δ-μm², %Δ-μm², or %Δμm², wherebythese units can be used interchangeably herein.

The “mode field diameter” or “MFD” of an optical fiber is determinedusing the Peterman II method, which is the current internationalstandard measurement technique for measuring the MFD of an opticalfiber. The MFD is given by:

${{MFD} = {2w}}{w = \lbrack {2\frac{\int_{0}^{\infty}{( {f(r)} )^{2}{rdr}}}{\int_{0}^{\infty}{( \frac{{df}(r)}{dr} )^{2}{rdr}}}} \rbrack^{1/2}}$where f(r) is the transverse component of the electric fielddistribution of the guided optical signal and r is radial position inthe fiber. The MFD depends on the wavelength of the optical signal andis reported for selected embodiments herein at wavelengths of 1310 nmand/or 1550 nm.

The “effective area” of an optical fiber is defined as:

$A_{eff} = \frac{2{\pi\lbrack {\int_{0}^{\infty}{( {f(r)} )^{2}{rdr}}} \rbrack}^{2}}{\int_{0}^{\infty}{( {f(r)} )^{4}{rdr}}}$where f(r) is the transverse component of the electric field of theguided optical signal and r is radial position in the fiber. In someembodiment, the effective area” or “A_(eff)” depends on the wavelengthof the optical signal and is understood to refer to wavelengths of 1310nm and 1550 nm as indicated herein.

The zero-dispersion wavelength is denoted λ₀ and is the wavelength for asingle mode fiber at which material dispersion and waveguide dispersioncancel. In some embodiments, in silica-based optical fibers, thezero-dispersion wavelength is about 1310 nm, e.g., between 1300 nm and1320 nm, depending on the dopants and refractive index profile used toform the optical fiber. Dispersion slope is the rate of change ofdispersion with respect to wavelength. Dispersion and dispersion slopeare reported for selected embodiments herein at a wavelength of 1310 nmand/or 1550 nm. Dispersion and dispersion slope are expressed in unitsof ps/nm-km and ps/nm²-km, respectively.

The cutoff wavelength of an optical fiber is the minimum wavelength atwhich the optical fiber will support only one propagating mode. Forwavelengths below (less than) the cutoff wavelength, multimodetransmission may occur and an additional source of dispersion(intermodal dispersion) may arise to limit the fiber's informationcarrying capacity. Cutoff wavelength will be reported herein as a fibercutoff wavelength (λ_(CF)) or a cable cutoff wavelength (λ_(CC)). Thecable cutoff wavelength is typically less than the fiber cutoffwavelength due to higher levels of bending and mechanical pressure inthe cable environment. The fiber cutoff wavelength λ_(CF) is based on a2-meter fiber length while the cable cutoff wavelength λ_(CC) is basedon a 22-meter cabled fiber length as specified in TIA-455-80: FOTP-80IEC-60793-1-44 Optical Fibres—Part 1-44: Measurement Methods and TestProcedures—Cut-off Wavelength (21 May 2003), by TelecommunicationsIndustry Association (TIA).

The “spring constant” λ_(p) of a primary coating is computed from thefollowing equation:

$\chi_{p} = \frac{E_{p}d_{g}}{t_{p}}$where E_(p) is the in situ modulus of the primary coating, t_(p) is thethickness of the primary coating, and d_(g) is the diameter 2r_(4b) ofthe glass fiber. The spring constant is a phenomenological parameterthat describes the extent to which the primary coating mitigatescoupling of the secondary coating to the glass fiber. (See “Relationshipof Mechanical Characteristics of Dual Coated Single Mode Optical Fibersand Microbending Loss”, by J. Baldauf et al., IEICE Transactions onCommunications, Vol. E76-B, No. 4, pp. 352-357 (1993)) In thephenomenological model, the buffering effect of the primary coating ismodeled as a spring with the spring constant given in the aboveequation. A low spring constant leads to greater resistance (lowersensitivity) to microbending. The tradeoff of in situ modulus andthickness in establishing the resistance of the primary coating tomicrobending is reflected in the spring constant.

The “operating wavelength”, λ_(op), of an optical fiber is thewavelength at which the optical fiber is operated. The operatingwavelength corresponds to the wavelength of a guided mode.Representative operating wavelengths include 850 nm, 1064 nm, 1310 nmand 1550 nm, which are commonly used in telecommunications systems,optical data links, and data centers. Although a particular operatingwavelength may be specified for an optical fiber, it is understood thata particular optical fiber can operate at multiple operating wavelengthsand/or over a continuous range of operating wavelengths. Characteristicssuch as modal bandwidth may vary with the operating wavelength and therelative refractive index profile of a particular optical fiber may bedesigned to provide optimal performance at a particular operatingwavelength, a particular combination of operating wavelengths, orparticular continuous range of operating wavelengths.

“Bandwidth” at a specified wavelength refers to overfilled launch (OFL)bandwidth at the specified wavelength as specified in the TIA/EIA455-204 and IEC 60793-1-41 standards.

The optical fibers disclosed herein include a core region, a claddingregion directly adjacent to and surrounding the core region, and acoating directly adjacent to and surrounding the cladding region. Thecladding region is a single homogeneous region or multiple regions thatdiffer in relative refractive index. The multiple cladding regions arepreferably concentric regions.

In some embodiments, the cladding region includes an inner claddingregion, a first outer cladding region directly adjacent to andsurrounding the inner cladding region, and a second outer claddingregion directly adjacent to and surrounding the first outer claddingregion. The relative refractive index of the inner cladding region maybe greater than, equal to, or less than the relative refractive index ofthe first outer cladding region. In embodiments without adepressed-index cladding region, an inner cladding region having a lowerrefractive index than the first outer cladding region is referred toherein as a trench or trench region.

In some embodiments, the cladding region includes a depressed-indexcladding region between and directly adjacent to an inner claddingregion and an outer cladding region, where the outer cladding regionincludes a first outer cladding region that surrounds and is directlyadjacent to the depressed-index cladding region and a second outercladding region that surrounds and is directly adjacent to the firstouter cladding region. The depressed-index cladding region is a claddingregion having a lower relative refractive index than the inner claddingand the first outer cladding region. The depressed-index cladding regionmay also be referred to herein as a trench or trench region. Thedepressed-index cladding region surrounds and is directly adjacent tothe inner cladding region. The depressed-index cladding region issurrounded by and directly adjacent to a first outer cladding region.The first outer cladding region is surrounded by and directly adjacentto a second outer cladding region. The depressed-index cladding regionmay contribute to a reduction in bending losses.

The core region, inner cladding region, depressed-index cladding region,first outer cladding region and second outer cladding region are alsoreferred to as core, inner cladding, depressed-index cladding, firstouter cladding, and second outer cladding, respectively. The innercladding, depressed-index cladding, first outer cladding, and secondouter cladding may independently have a positive or negative relativerefractive index. The core preferably has a positive relative refractiveindex. Preferred values for relative refractive index for each of theregions are given below.

Whenever used herein, radial position r₁ and relative refractive indexΔ₁ or Δ₁(r) refer to the core region, radial position r₂ and relativerefractive index Δ₂ or Δ₂(r) refer to the inner cladding region, radialposition r₃ and relative refractive index Δ₃ or Δ₃(r) refer to thedepressed-index cladding region, radial position r_(4a) and relativerefractive index Δ_(4a) or Δ_(4a)(r) refer to the first outer claddingregion, radial position r_(4b) and relative refractive index Δ_(4b) orΔ_(4b)(r) refer to the second outer cladding region, radial position r₅refers to the primary coating, radial position r₆ refers to thesecondary coating, and radial position r₇ refers to the optionaltertiary coating.

The relative refractive index Δ₁(r) has a maximum value Δ_(1max) and aminimum value Δ_(1min). The relative refractive index Δ₂(r) has amaximum value Δ_(2max) and a minimum value Δ_(2min). The relativerefractive index Δ₃(r) has a maximum value Δ_(3max) and a minimum valueΔ_(3min). The relative refractive index Δ_(4a)(r) has a maximum valueΔ_(4amax) and a minimum value Δ_(4amin). The relative refractive indexΔ_(4b)(r) has a maximum value Δ_(4bmax) and a minimum value Δ_(4bmin).In embodiments in which the relative refractive index is constant orapproximately constant over a region, the maximum and minimum values ofthe relative refractive index are equal or approximately equal. Unlessotherwise specified, if a single value is reported for the relativerefractive index of a region, the single value corresponds to an averagevalue for the region.

It is understood that the central core region is substantiallycylindrical in shape and that a surrounding inner cladding region, asurrounding depressed-index cladding region, a surrounding outercladding region, a surrounding primary coating, a surrounding secondarycoating, and a surrounding tertiary coating are substantially annular inshape. Annular regions are characterized in terms of an inner radius andan outer radius. Radial positions r₁, r₂, r₃, r_(4a), r_(4b), r₅, r₆,and r₇ refer herein to the outermost radii of the core, inner cladding,depressed-index cladding, first outer cladding, second outer cladding,primary coating, secondary coating, and tertiary coating, respectively.Radius r_(4b) corresponds to the outer radius of the glass portion ofthe optical fiber and is also referred to as the “cladding radius”.“Cladding diameter” refers to twice the cladding radius and correspondsto 2r_(4b). The radius r₆ corresponds to the outer radius of the opticalfiber in embodiments without a tertiary coating. When a tertiary coatingis present, the radius r₇ corresponds to the outer radius of the opticalfiber.

When two regions are directly adjacent to each other, the outer radiusof the inner of the two regions coincides with the inner radius of theouter of the two regions. In one embodiment, for example, the fiberincludes a depressed-index cladding region surrounded by and directlyadjacent to a first outer cladding region. In such an embodiment, theradius r₃ corresponds to the outer radius of the depressed-indexcladding region and the inner radius of the first outer cladding region.In embodiments in which the relative refractive index profile includes adepressed-index cladding region surrounding and directly adjacent to aninner cladding region, the radial position r₂ corresponds to the outerradius of the inner cladding region and the inner radius of thedepressed-index cladding region. In embodiments in which the relativerefractive index profile includes a depressed-index cladding regionsurrounding and directly adjacent to the core, the radial position r₁corresponds to the outer radius of the core and the inner radius of thedepressed-index cladding region.

The following terminology applies to embodiments in which the relativerefractive index profile includes an inner cladding region surroundingand directly adjacent to the core, a depressed-index cladding regionsurrounding and directly adjacent to the inner cladding region, a firstouter cladding region surrounding and directly adjacent to thedepressed-index cladding region, a second outer cladding regionsurrounding and directly adjacent to the first outer cladding region, aprimary coating surrounding and directly adjacent to the second outercladding region, and a secondary coating surrounding and directlyadjacent to the primary coating. The difference between radial positionr₂ and radial position r₁ is referred to herein as the thickness of theinner cladding region. The difference between radial position r₃ andradial position r₂ is referred to herein as the thickness of thedepressed-index cladding region. The difference between radial positionr_(4a) and radial position r₃ is referred to herein as the thickness ofthe first outer cladding region. The difference between radial positionr_(4b) and radial position r_(4a) is referred to herein as the thicknessof the second outer cladding region. The difference between radialposition r₅ and radial position r_(4b) is referred to herein as thethickness of the primary coating. The difference between radial positionr₆ and radial position r₅ is referred to herein as the thickness of thesecondary coating.

The following terminology applies to embodiments in which an innercladding region is directly adjacent to a core region, a first outercladding region directly adjacent to the core region, and a second outercladding region is directly adjacent The first outer cladding region.The difference between radial position r₂ and radial position r₁ isreferred to herein as the thickness of the inner cladding region. Thedifference between radial position r_(4a) and radial position r₂ isreferred to herein as the thickness of the first outer cladding region.The difference between radial position r_(4b) and radial position r_(4a)is referred to herein as the thickness of the second outer claddingregion. The difference between radial position r₅ and radial position r₄is referred to herein as the thickness of the primary coating. Thedifference between radial position r₆ and radial position r₅ is referredto herein as the thickness of the secondary coating.

The following terminology applies to embodiments in which the relativerefractive index profile lacks both an inner cladding region and adepressed-index cladding region. The difference between radial positionr_(4a) and radial position r₁ is referred to herein as the thickness ofthe first outer cladding region. The difference between radial positionr_(4b) and radial position r_(4a) is referred to herein as the thicknessof the second outer cladding region. The difference between radialposition r₅ and radial position r_(4b) is referred to herein as thethickness of the primary coating. The difference between radial positionr₆ and radial position r₅ is referred to herein as the thickness of thesecondary coating.

The coatings described herein are formed from curable coatingcompositions. Curable coating compositions include one or more curablecomponents. As used herein, the term “curable” is intended to mean thatthe component, when exposed to a suitable source of curing energy,includes one or more curable functional groups capable of formingcovalent bonds that participate in linking the component to itself or toother components of the coating composition. The product obtained bycuring a curable coating composition is referred to herein as the curedproduct of the composition. The cured product is preferably a polymer.The curing process is induced by energy. Forms of energy includeradiation or thermal energy. In a preferred embodiment, curing occurswith radiation, where radiation refers to electromagnetic radiation.Curing induced by radiation is referred to herein as radiation curing orphotocuring. A radiation-curable component is a component that can beinduced to undergo a curing reaction when exposed to radiation of asuitable wavelength at a suitable intensity for a sufficient period oftime. Suitable wavelengths include wavelengths in the infrared, visible,or ultraviolet portion of the electromagnetic spectrum. The radiationcuring reaction occurs in the presence of a photoinitiator. Aradiation-curable component may also be thermally curable. Similarly, athermally curable component is a component that can be induced toundergo a curing reaction when exposed to thermal energy of sufficientintensity for a sufficient period of time. A thermally curable componentmay also be radiation curable.

A curable component includes one or more curable functional groups. Acurable component with only one curable functional group is referred toherein as a monofunctional curable component. A curable component havingtwo or more curable functional groups is referred to herein as amultifunctional curable component. Multifunctional curable componentsinclude two or more functional groups capable of forming covalent bondsduring the curing process and can introduce crosslinks into thepolymeric network formed during the curing process. Multifunctionalcurable components may also be referred to herein as “crosslinkers” or“curable crosslinkers”. Curable components include curable monomers andcurable oligomers. Examples of functional groups that participate incovalent bond formation during the curing process are identifiedhereinafter.

The term “molecular weight” when applied to polyols means number averagemolecular weight (M_(n)).

The term “(meth)acrylate” means methacrylate, acrylate, or a combinationof methacrylate and acrylate.

Values of in situ modulus, Young's modulus, % elongation, and tearstrength refer to values as determined under the measurement conditionsby the procedures described herein.

As described in the background section, optical fiber designs withreduced coating diameters have been proposed, but the cladding diameterof such fibers is maintained at the conventional value of 125 μm.Decreasing the cladding diameter to 90 μm or smaller may increase themicrobending sensitivity by an order of magnitude compared to fiberswith cladding diameters of 125 μm, and the coating solutions of thecurrent optical fiber designs are not sufficient to achieve lowattenuation and low bend losses. Specifically, commercially-availablesingle mode optical fibers with small cladding diameters and smallcoated fiber diameters suffer from increased microbending losses unlessthe numerical aperture is increased or the core diameter is decreased,both of which negatively impact the compatibility with transceivers andconventional single mode optical fibers. Improving microbending lossesfor the single mode optical fibers has been difficult if the totalthickness of the primary and secondary coatings has a smaller value thanthe 58.5-62.5 μm thickness used for standard telecommunication fibers.Decreasing the modulus of the primary coating can help reduce themicrobending sensitivity of the fiber, as can increasing the thicknessof the primary coating, but the thickness of the primary coating canonly be increased if there is a concomitant decrease in the thickness ofsecondary coating given the constraint on the total thickness of the twocoating layers. Decreasing the secondary coating thickness isundesirable because it reduces puncture resistance of the coated fiber.It is therefore desirable to design a single mode optical fiber havingreduced cladding and coating diameters, low attenuation, low bendlosses, a G.657-compliant mode field diameter and a low cutoffwavelength.

Embodiments of the present description relate to a reduced-diametersingle mode optical fiber with small outer coating diameters (e.g., 2r₆or 2r₇≤180 μm), and a small cladding diameter (e.g., 2r_(4b)≤90 μm). Thedisclosed reduced-diameter single mode optical fiber can have goodmicrobending properties and good resistance to puncture if thethicknesses t_(P) of the primary coating and the thickness is of thesecondary coating are each at least about 10 μm. In some embodiments,the relative coating thickness, t_(P)/t_(S), is in the range0.5≤t_(P)/t_(S)≤1.5. The disclosed reduced-diameter single mode opticalfiber can be deployed in tight bends, at a radius equal to or less than1.5 mm for an 82 degree bend.

The disclosed reduced-diameter single mode optical fiber is suitable fordata center applications and features high modal bandwidth, lowattenuation, low microbending sensitivity, and puncture resistance in acompact form factor. The disclosed single mode optical fibers have anincreased reliability of being routed through extremely tight bendconfigurations or bend in a small radius arc inside a fiber array unitthat couples an array of fibers to arrays of lasers and photodiodes. Thedisclosed single mode optical fibers comprise a second outer claddingregion doped with titanium to improve mechanical integrity by increasingthe value of the fatigue constant. In some embodiments, the reliabilityis further enhanced by a reduction in the diameter of the second outercladding region 2r_(4b) to 90 μm or less (e.g., or 85 μm or less, or 80μm or less, or 75 μm or less).

The disclosed single mode optical fibers also possess large mode fielddiameters without experiencing significant bending-induced signaldegradation. The disclosed single mode optical fibers have an overfilledlaunch (OFL) bandwidth greater than 200 MHz-km (e.g., greater than 300MHz-km, greater than 400 MHz-km, greater than 500 MHz-km, greater than1000 MHz-km, greater than 2000 MHz-km, greater than 4000 MHz-km, etc.)at a wavelength 850 nm, 980 nm, 1064 nm and/or 1300 nm.

Reference will now be made in detail to illustrative embodiments of thepresent description.

One aspect of the present disclosure relates to a single mode opticalfiber. FIG. 1 is a side elevated view of a section of an exemplarysingle mode optical fiber, according to some embodiments. As shown, thesingle mode optical fiber 100 comprises a glass core region (“core”) 10that is centered on the centerline AC. The core 10 can be immediatelysurrounded by a glass cladding region (“cladding”) 50. The cladding 50can be immediately surrounded by a protective coating 70 made of anon-glass material, such as a polymeric material.

Referring to FIG. 2 , a cross-sectional view of an exemplary single modeoptical fiber 100 is shown in a cross sectional view in x-y plane, inaccordance with some embodiments of the present disclosure.

As shown, the single mode optical fiber 100 includes a waveguiding glassfiber surrounded by a protective coating 70 (hereinafter “coating”). Theglass fiber includes a higher index core region 10 (hereinafter “core”)surrounded by a lower index cladding region 50 (hereinafter “cladding”).In some embodiments, the coating 70 typically includes a primary coatingwith low modulus in contact with the glass fiber and a secondary coatingwith high modulus that surrounds and contacts the primary coating. Thesecondary coating provides mechanical integrity and allows the singlemode optical fiber 100 to be handled for processing and installation incables, while the primary coating acts to dissipate external forces toprevent The external forces from being transferred to the glass fiber.By dampening the external forces, the primary coating prevents damage tothe glass fiber and minimizes attenuation of optical signals caused bymicrobending.

As illustrated, the core 10 has a radius r₁ and a relative refractiveindex Δ₁. The cladding 50 can be directly adjacent to and surroundingthe core 10. In some embodiments, the cladding 50 includes an innercladding region (“inner cladding”) 52 directly adjacent to andsurrounding the core 10, a depressed-index cladding region(“depressed-index cladding”) 54 directly adjacent to and surrounding theinner cladding 52, and a first outer cladding region (“first outercladding”) 56 directly adjacent to and surrounding the depressed-indexcladding 54, and a second outer cladding region (“second outercladding”) 58 directly adjacent to and surrounding the first outercladding 56. The inner cladding 52 extends from the radius r₁ to aradius r₂ and has a relative refractive index Δ₂. The depressed-indexcladding 54 extends from the radius r₂ to a radius r₃ and has a relativerefractive index Δ₃. The first outer cladding 56 extends from the radiusr₃ to a radius r_(4a) and has a relative refractive index Δ_(4a) whilethe second outer cladding 58 extends from the radius r_(4a) to a radiusr_(4b) and has a relative refractive index Δ_(4b).

In some alternative embodiments not shown in the figures, thedepressed-index cladding 54 can be omitted. That is, the cladding 50includes only three cladding regions. The inner cladding 52 is directlyadjacent to and surrounds the core 10, extends from the radius r₁ to aradius r₂, and has a relative refractive index Δ₂. The first outercladding 56 is directly adjacent to and surrounds the inner cladding 52,extends from the radius r₂ to a radius r_(4a), and has a relativerefractive index Δ_(4a). The second outer cladding 58 is directlyadjacent to and surrounds the first outer cladding 56, extends from theradius r_(4a) to a radius r_(4b), and has a relative refractive indexΔ_(4b).

In some other alternative embodiments not shown in the figures, theinner cladding 52 and the depressed-index cladding 54 can be omitted.That is, the cladding 50 includes only two outer cladding regions. Thefirst outer cladding 56 is directly adjacent to and surrounding the core10, extends from the radius r₁ to a radius r_(4a), and has a relativerefractive index Δ_(4a). The second outer cladding 58 is directlyadjacent to and surrounds the first outer cladding 56, extends from theradius r_(4a) to a radius r_(4b), and has a relative refractive indexΔ_(4b).

Protective coating 70 is directly adjacent to and surrounds the cladding50. In some embodiments, the protective coating 70 includes a primarycoating 72 and a secondary coating 74. The primary coating 72 and thesecondary coating 74 are typically formed by applying a curable coatingcomposition to the glass fiber as a viscous liquid and curing. In someembodiments, the protective coating 70 may also include a tertiarycoating 76 that surrounds the secondary coating 74.

The secondary coating 74 is a harder material (higher Young's modulus)than the primary coating 72 and is designed to protect the glass fiberfrom damage caused by abrasion or external forces that arise duringprocessing, handling, and installation of the optical fiber. The primarycoating 72 is a softer material (lower Young's modulus) than thesecondary coating 74 and is designed to buffer or dissipates stressesthat result from forces applied to the outer surface of the secondarycoating 74.

The primary coating 72 dissipates shear forces and minimizes the stressthat reaches the glass fiber (which includes the core 10 and thecladding 50). The primary coating 72 is especially important indissipating shear forces that arise due to the microbends that theoptical fiber encounters when deployed in a cable. The primary coating72 should maintain adequate adhesion to the glass fiber during thermaland hydrolytic aging, yet be strippable from the glass fiber forsplicing purposes.

The optional tertiary coating 76 may include pigments, inks or othercoloring agents to mark the optical fiber for identification purposesand typically has a Young's modulus similar to the Young's modulus ofthe secondary coating 74.

Another aspect of the present disclosure relates to an optical fiberribbon. FIG. 3 illustrates a cross-sectional view of an exemplaryoptical fiber ribbon 300 in accordance with some embodiments of thepresent disclosure. As illustrated, the optical fiber ribbon 300includes a plurality of optical fibers 100 and a matrix 320encapsulating the plurality of optical fibers 100. Each optical fiber100 includes a core, a cladding, and a protective coating as describedabove. The ribbon matrix 320 can be formed from the same compositionused to prepare a secondary coating, or the ribbon matrix 320 can beformed from a different composition that is otherwise compatible foruse.

The optical fibers 100 are aligned relative to one another in asubstantially planar and parallel relationship. The optical fibers 100in the optical fiber ribbon 300 are encapsulated by the ribbon matrix320 in any suitable configuration (e.g., edge-bonded ribbon,thin-encapsulated ribbon, thick-encapsulated ribbon, or multi-layerribbon) by any suitable fabricating methods. In FIG. 3 , the fiber opticribbon 300 contains twelve (12) optical fibers 100; however, it shouldbe apparent to those skilled in the art that any number of opticalfibers 100 (e.g., two or more) may be employed to form fiber opticribbon 300 disposed for a particular use.

Another aspect of the present disclosure relates to an optical fibercable. FIG. 4 illustrates a cross-sectional view of an exemplary opticalfiber cable 400. Cable 400 includes a plurality of optical fibers 100surrounded by jacket 430. Optical fibers 100 may be densely or looselypacked into a conduit enclosed by inner surface of jacket 430. Thenumber of fibers placed in the jacket 430 is referred to as the “fibercount” of optical fiber cable 400. The jacket 430 is formed from anextruded polymer material and may include multiple concentric layers ofpolymers or other materials. Optical fiber cable 400 may include one ormore strengthening members (not shown) embedded within jacket 430 orplaced within the conduit defined by the inner surface of jacket 430.Strengthening members include fibers or rods that are more rigid thanjacket 430. The strengthening member is made from metal, braided steel,glass-reinforced plastic, fiberglass, or other suitable material.Optical fiber cable 400 may include other layers surrounded by jacket430 (e.g. armor layers, moisture barrier layers, rip cords, etc.).Optical fiber cable 400 may have a stranded, loose tube core or otherfiber optic cable construction.

Fiber Coupling and Minimum Bend Radius

One challenging problem is to couple light from a silicon photonicdevice (e.g., a waveguide or VCSEL) to the single mode optical fiberwith low cost. Referring to FIG. 5 , an optical coupling 500 is shown,according to some embodiments. Elements of FIG. 5 that share numberswith those of FIGS. 1-4 may have the same structure and function asdescribed herein in reference to FIGS. 1-4 . In some embodiments,optical coupling 500 comprises a single mode optical fiber 100, awaveguide 502 on a substrate 508, and a grating 504. Optical coupling500 may further comprise a connector structure 506.

In some embodiments, grating 504 may allow light to transmit fromwaveguide 502 (e.g., silicon waveguide) to single mode optical fiber 100and/or vice versa (e.g., optical coupling). Connector structure 506 maybe used to protect, support, and/or guide single mode optical fiber 100close to where single mode optical fiber 100 interfaces with waveguide502. Depending on volume requirements (e.g., tight spaces at datacenters, the space above waveguide 502 being about 4-5 mm or less),single mode optical fiber 100 may be bent with approximately a quarterof turn (e.g., approximately 82-degree arc) at bend radius ofapproximately 2.5 mm or less, for example≤1.5 mm. Connector structure506 may be, for example, a glass or ceramic ferrule with curved hole.The fiber-guiding geometry of connector structure 506 may be curved suchthat it matches a desired bend radius, r_(b), for single mode opticalfiber 100. It should be appreciated that the bend radius r_(b) mayrepresent an average radius (e.g., if the fiber-guiding geometry has anon-constant radius of curvature). Single mode optical fiber 100 may bestripped of the coating down to the glass cladding, and the strippedportion inserted into the hole of connector structure 506 and glued withan epoxy. Typically, ordinary comparative optical fibers fiber maybecome easily damaged during stripping. Subsequently, the fiberinsertion process may cause single mode optical fiber 100 to break(e.g., insertion failure). Insertion failure may result from flow stress(e.g., the stress at which a wire structure deforms plastically) inducedby a small bend radius r_(b). Under stress, surface defects imposed onordinary comparative optical fibers may propagate deeper into the glassof the optical fiber, causing mechanical failure (fiber break) and/orshortened life cycle of the product. However, embodiments disclosedherein provide optical fibers that can be coupled to photonic deviceseven when bent to radii of 3 mm or less while providing robustnessagainst mechanical failure or degradation. By reducing the bend radiusr_(b), the volume of optical coupling 500 may be made smaller (e.g.,connector structure 506 may be made smaller), which in turn increasesthe number of fiber connections capable of being housed in a given spaceof a data center.

In some embodiments, the single mode optical fibers 100 disclosed hereincan be coupled to silicon photonic device and having sufficientreliability when deployed inside an approximately 90-degree bend fiberarray unit (FAU), even when bent to radii of 2.5 mm or less withoutmechanical failure due or fiber break, which have a minimum bend radiusin the 1.5-2 mm range, even tighter bends are possible from areliability standpoint if the cladding also includes a second outercladding doped with titanium. The disclosed single mode optical fibers100 can be advantageously inserted through the hole in the couplingstructure 506 that has a bend radius r_(b) of approximately 2.5 mm orless (e.g., 1.5 mm≤r_(b)≤2.5 mm), without succumbing to mechanicalfailure or degradation, and thus can be bent to a such a small diameterwithout substantial loss of strength or significant loss of lifetime.Single mode optical fibers 100 advantageously have improved surfacedamage resistance and low bending loss.

It is noted that, strategies for reducing the diameter of the singlemode optical fiber 100 include reducing the diameter of glass fiber andreducing the thickness of the primary and/or secondary coating. In somesituations, these strategies may lead to compromises in the performanceof the single mode optical fiber 100. For example, a smaller outercladding diameter tends to increase the microbending sensitivity and toincrease attenuation of the optical signal propagating in the core. Asanother example, decreasing the outer cladding diameter from 125 μm to90 μm may lead to an increase in microbending sensitivity by about anorder of magnitude in current optical fiber designs. As yet anotherexample, thinner primary coatings may be more susceptible toshear-induced defects during processing, while thinner secondarycoatings may be more susceptible to punctures.

The disclosed single mode optical fiber 100 can have smaller outercladding diameters, which enable the single mode optical fiber 100 to bedeployed in tight bends, at a radius as small as 1.5 μm for an 82-degreebend.

Further, a titanium-doped outer cladding can be used for more increasedreliability requirement (resistance to fracture or fatigue), such aseven smaller bend radii for a given arc length, or multiple bendconditions at a given bend radius, or a longer lifetime at a given arclength or given bend radius, etc. Therefore, the disclosed single modeoptical fiber 100 can have a high transmission capacity, a smalldiameter, a low transmission loss, good microbending properties, highpuncture resistance, and high reliability.

FIG. 6 illustrates a plot of the relationship between minimum bendradius (mm) and cladding diameter (μm) for an 82-degree bend condition.The vertical axis of the graph represents a bend radius r_(b) (see FIG.5 ), in mm, of an optical fiber. The horizontal axis represents anoutermost diameter, in μm, of the cladding of the optical fiber (e.g.,2r_(4b) for fibers with first and second outer cladding regions asdescribed herein). The data that makes up the plots includes modeled andexperimentally derived data and extrapolations. The plot in FIG. 6regards configurations, for a single mode optical fiber 100 (e.g., FIGS.1-4 ) being bent in a single 82-degree (approximately) arc, of theoptical fiber in which the probability of failure of the optical fiberover a 5-year lifetime is 10⁻¹⁰ or less (i.e., the expectant lifetime ofthe bent optical fiber 100 is at least 5 years).

For describing embodiments with respect to FIG. 6 , as a non-limitingexample, reference is made to structures of single mode optical fiber100 in FIG. 2 . In some embodiments, plot 610 indicates the long termreliability limits of a comparative optical fiber having notitania-doped outer cladding (e.g., a comparative fiber in which thefirst outer cladding 56 is undoped silica and the second outer cladding58 is undoped silica) based on both modelling and experiment. Plot 610shows that, when the comparative optical fiber has an outermost diameterof cladding 50 of approximately 125 μm, the comparative optical fibermay be bent to a bend radius of approximately 2.3 mm with 10⁻¹⁰probability of failure over a 5-year lifetime. Bending of thecomparative optical fiber with an outermost cladding diameter of 125 μmto a bend radius of less than approximately 2.3 mm reduces the lifetimeof the comparative optical fiber to less than 5 years. Plot 610 showsthat the relationship between bend radius and outermost claddingdiameter is linear for the given conditions (i.e., approximately82-degree bend arc and tolerance 10⁻¹⁰ probability of failure over a5-year). Following the linear relationship, plot 610 shows that, whenthe comparative optical fiber has an outer diameter of cladding 50 ofapproximately 100 μm, the comparative optical fiber may be bent to abend radius of approximately 1.9 mm with 10⁻¹⁰ probability of failureover a 5-year lifetime. Plot 610 shows that, when the comparativeoptical fiber has an outer diameter of cladding 50 of approximately 80μm, the comparative optical fiber may be bent to a bend radius ofapproximately 1.5 mm (with 10⁻¹⁰ probability of failure over a 5-yearlifetime). Plot 610 shows that, when the comparative optical fiber hasan outer diameter of cladding 50 of approximately 62.5 μm, thecomparative optical fiber may be bent to a bend radius of approximately1.2 mm (with 10⁻¹⁰ probability of failure over a 5-year lifetime). Plot610 shows that, when the comparative optical fiber has an outer diameterof cladding 50 of approximately 53 μm, the comparative optical fiber maybe bent to a bend radius of approximately 1 mm (with 10⁻¹⁰ probabilityof failure over a 5-year lifetime).

Embodiments described herein employ titania-doped silica as a secondouter cladding to increase robustness of an optical fiber at smallerbend radii. In some embodiments, plot 620 indicates the long termreliability limits of optical fiber 100 having a titania-doped outercladding with a titania concentration about 8 wt %. Plot 620 shows that,when optical fiber 100 has an outer diameter of cladding 50 ofapproximately 125 μm, optical fiber 100 may be bent to a bend radius ofapproximately 1.5 mm (with 10⁻¹⁰ probability of failure over a 5-yearlifetime). Plot 620 shows that, when optical fiber 100 has an outerdiameter of cladding 50 of approximately 80 μm, optical fiber 100 may bebent to a bend radius of approximately 1 mm (with 10⁻¹⁰ probability offailure over a 5-year lifetime). Such decreasing in the minimumallowable deployment bend radius (consistent with an expected 5-yearlifetime) relative to the undoped silica-clad comparative fiber is dueto titania doping of the second outer cladding region, which providehigher breaking stresses and increased fatigue resistance value (e.g.,in a range from 26 to 32 instead of about 20 for undoped silica), whichis a measure of a material's susceptibility to subcritical crack growthunder stress.

The disclosed single mode optical fibers 100 has an improved fiberreliability, which is important for being able to deploy the single modeoptical fibers 100 in short reach (e.g., fiber length less than 10 m, orless than 1 m, or between 1 cm and 1 m, or between 1 cm to 50 cm, orbetween 1 cm to 25 cm, etc.) interconnects within data centers,especially when the single mode optical fiber 100 is routed inconfigurations with effective bend radii r_(b) less than 4.0 mm, or lessthan 3.0 mm, or less than 2.5 mm, etc. The short reach interconnectstypically have a fairly short usage lifetime (e.g., 3-5 years) inpractice, which is the same lifetime as the electronic equipment theywill be connected to. These very short reach interconnects can bedeployed within a rack or even within a server.

Relative Refractive Index Profiles

In some embodiments, the single mode optical fiber 100 can have a numberof different physical configurations defined by way of example as arelative refractive index profile. One type of the disclosed opticalfiber is a graded-index fiber, which has a core region with a refractiveindex that varies with distance from the fiber center. Examples ofgraded-index fibers include fibers having a core with a relativerefractive index having an α-profile defined above or a super-Gaussianrelative refractive index profile. Examples of the graded-index fibersare set forth below in connection with FIGS. 7A-7E.

Referring to FIG. 7A, a plot of the relative refractive index Δ% (r)versus the radial coordinate illustrating a first exemplary physicalconfiguration of a graded-index fiber, according to some embodiments. Asshown, the core 10 having a radius r₁ can have a graded refractive indexdefined by described by an α-profile. The radial position r₀(corresponding to Δ_(1max)) of the α-profile corresponds to thecenterline AC (r=0) of the fiber and the radial position r_(z) of theα-profile corresponds to the core radius r₁. In some embodiments with acenterline dip, the radial position r₀ is slightly offset from thecenterline AC of the fiber.

In some embodiments, the core 10 is immediately surrounded by thecladding 50 that extends from the radius r₁ to a radius r_(4b). Thecladding 50 can include a first outer cladding region 56 surrounding thecore 10, and a second outer cladding region 58 surrounding the firstouter cladding region 56. The first outer cladding region 56 can be apure silica cladding or a SiO₂ cladding extending from the radius r₁ toa radius r_(4a) and having a relative refractive index Δ_(4a) that issubstantially zero. The second outer cladding region 58 can be anup-doped cladding extending from the radius r_(4a) to the radius r_(4b),and having a relative refractive index Δ_(4b). In some embodiments, thesecond outer cladding region 58 is a silica based glass doped withtitania. In some embodiments, Δ_(4b) is larger than Δ_(1max).

FIG. 7B is a plot of the relative refractive index Δ% (r) versus theradial coordinate illustrating a second exemplary physical configurationof a graded-index fiber, according to some embodiments. The core 10having a radius r₁ can have a graded refractive index defined bydescribed by an α-profile. The core 10 is immediately surrounded by thecladding 50 that extends from the radius r₁ to a radius r_(4b). Thecladding 50 includes an inner cladding region 52, a first outer claddingregion 56 surrounding the core 10, and a second outer cladding region 58surrounding the first outer cladding region 56. The inner claddingregion 52 can be a down-doped cladding extending from the radius r₁ to aradius r₂ and having a negative relative refractive index Δ₂. The firstouter cladding region 56 can be a pure silica cladding or a doped SiO₂cladding extending from the radius r₂ to a radius r_(4a) and having arelative refractive index Δ_(4a), which in one embodiment issubstantially zero. The second outer cladding region 58 can be anup-doped cladding extending from the radius r_(4a) to the radius r_(4b),and having a relative refractive index Δ_(4b). In some embodiments, thesecond outer cladding region 58 is a silica based glass doped withtitania. In some embodiments, Δ_(4b) is larger than Δ_(1max).

FIG. 7C is a plot of the relative refractive index Δ% (r) versus theradial coordinate illustrating a third exemplary physical configurationof a graded-index fiber, according to some embodiments. The core 10having a radius r₁ can have a graded refractive index defined bydescribed by an α-profile. The core 10 is immediately surrounded by thecladding 50 that extends from the radius r₁ to a radius r_(4b). Thecladding 50 includes an inner cladding region 52, a depressed-indexcladding 54 directly adjacent to and surrounding the inner cladding 52,a first outer cladding region 56 directly adjacent to and surroundingthe depressed-index cladding 54, and a second outer cladding region 58directly adjacent to and surrounding the first outer cladding region 56.The inner cladding region 52 can be a pure silica cladding or a SiO₂cladding extending from the radius r₁ to a radius r₂ and having arelative refractive index Δ₂. The depressed-index cladding 54 can be adown-doped silica cladding extending from the radius r₂ to a radius r₃and having a negative relative refractive index Δ₃. The first outercladding region 56 can be a pure silica cladding extending from theradius r₁ to a radius r_(4a) and having a relative refractive indexΔ_(4a) that is substantially zero. The second outer cladding region 58can be an up-doped cladding extending from the radius r_(4a) to theradius r_(4b), and having a relative refractive index Δ_(4b). In someembodiments, the second outer cladding region 58 is a silica based glassdoped with titania. In some embodiments, Δ_(4b) is larger than Δ_(1max).The relative refractive index Δ₃ is less than the relative refractiveindex Δ₂ and less than the relative refractive index Δ_(4a). Therelative refractive index Δ_(4b) is greater than the relative refractiveindex Δ_(4a). In some embodiments, the relative refractive index Δ₂ isless than the relative refractive index Δ_(4a) and in other embodiments,the relative refractive index Δ₂ is greater than or equal to therelative refractive index Δ_(4a).

FIG. 7D is a plot of the relative refractive index Δ% (r) versus theradial coordinate illustrating a fourth exemplary physical configurationof a step-index fiber, according to some embodiments. The core 10 havinga radius r₁ can have a step refractive index Δ₁. The core 10 isimmediately surrounded by the cladding 50 that extends from the radiusr₁ to a radius r_(4b). The cladding 50 includes an inner cladding region52, a depressed-index cladding 54 directly adjacent to and surroundingthe inner cladding 52, a first outer cladding region 56 directlyadjacent to and surrounding the depressed-index cladding 54, and asecond outer cladding region 58 directly adjacent to and surrounding thefirst outer cladding region 56. The inner cladding region 52 can be apure silica cladding or a SiO₂ cladding extending from the radius r₁ toa radius r₂ and having a relative refractive index Δ₂. The boundarybetween Δ₁ and Δ₂ may be a step boundary. It should be appreciated thata step change is an idealization and that a change in relativerefractive index at an interface between two materials may not bestrictly vertical in practice. Instead, a change in relative refractiveindex at an interface between two materials may have a slope orcurvature. The depressed-index cladding 54 can be a down-doped silicacladding extending from the radius r₂ to a radius r₃ and having anegative relative refractive index Δ₃. The first outer cladding region56 can be a pure silica cladding extending from the radius r₁ to aradius r_(4a) and having a relative refractive index Δ_(4a) that issubstantially zero. The second outer cladding region 58 can be anup-doped cladding extending from the radius r_(4a) to the radius r_(4b),and having a relative refractive index Δ_(4b). In some embodiments, thesecond outer cladding region 58 is a silica based glass doped withtitania. In some embodiments, Δ_(4b) is larger than Δ_(1max). Therelative refractive index Δ₃ is less than the relative refractive indexΔ₂ and less than the relative refractive index Δ_(4a). The relativerefractive index Δ_(4b i)s greater than the relative refractive indexΔ_(4a). In some embodiments, the relative refractive index Δ₂ is lessthan the relative refractive index Δ_(4a) and in other embodiments, therelative refractive index Δ₂ is greater than or equal to the relativerefractive index Δ_(4a).

FIG. 7E is a plot of the relative refractive index Δ% (r) versus theradial coordinate illustrating a fifth exemplary physical configurationof a graded-index fiber, according to some embodiments. The core 10having a radius r₁ can have a graded refractive index defined bydescribed by an α-profile. The core 10 is immediately surrounded by thecladding 50 that extends from the radius r₁ to a radius r_(4b). Thecladding 50 includes an inner cladding region 52, a depressed-indexcladding 54 directly adjacent to and surrounding the inner cladding 52,a first outer cladding region 56 directly adjacent to and surroundingthe depressed-index cladding 54, and a second outer cladding region 58directly adjacent to and surrounding the first outer cladding region 56.The inner cladding region 52 can be a down-doped silica cladding or aSiO₂ cladding extending from the radius r₁ to a radius r₂ and having anegative relative refractive index Δ₂. The depressed-index cladding 54can be a down-doped silica cladding extending from the radius r₂ to aradius r₃ and having a negative relative refractive index Δ₃ which isless than the relative refractive index Δ₂. The first outer claddingregion 56 can be a pure silica cladding extending from the radius r₁ toa radius r_(4a) and having a relative refractive index Δ_(4a) that issubstantially zero. The second outer cladding region 58 can be anup-doped cladding extending from the radius r_(4a) to the radius r_(4b),and having a relative refractive index Δ_(4b). In some embodiments, thesecond outer cladding region 58 is a silica based glass doped withtitania. In some embodiments, the relative refractive index Δ_(4a) issubstantially zero. The relative refractive index Δ_(4b) is greater thanthe relative refractive index Δ_(1max).

Parameter Specifications of Properties

In some embodiments, various fiber parameters described herein can beproperly designed to increase transmission capacity, puncture resistanceand microbending performance. In the following, details of variousdesigns of the fiber parameters are described below. It is noted that,the following numerical values for fiber parameters can be applied tofibers with either step-index cores or graded-index cores described, forexample, above in connection with FIGS. 7A-7E.

Referring again optical fiber 100 in FIG. 2 as a non-limiting example,in some embodiments, core 10 comprises silica glass. The silica glass ofthe core region may be Ge-free; that is the core region comprises silicaglass that lacks Ge. The silica glass of core 10 may be undoped silicaglass, updoped silica glass, and/or downdoped silica glass. Updopedsilica glass may include silica glass doped with an alkali metal oxide(e.g. Na₂O, K₂O, Li₂O, Cs₂O, or Rb₂O). Downdoped silica glass mayinclude silica glass doped with F. In some embodiments, core 10 isco-doped with alkali metal oxide and fluorine. The concentration of K₂Oin core 10, expressed in terms of the amount of K, may be in the rangefrom 20 ppm to 1000 ppm, or 35 ppm to 500 ppm, or 50 ppm to 300 ppm,where ppm refers to parts per million by weight. Alkali metal oxidesother than K₂O may be present in amounts corresponding to the equivalentmolar amount of K₂O as determined from the amount of K indicated above

In some embodiments, core 10 may include an updopant and/or adowndopant. The concentration of updopant may be highest at thecenterline (r=0) and lowest at the radius r₁. In some embodiments, theconcentration of downdopant may be lowest at the centerline (r=0) andhighest at the radius r₁. In some embodiments, the relative refractiveindex Δ₁ can have a positive value near the centerline (r=0) anddecrease to a negative value at the radius r₁.

In some embodiment, core 10 may be a segmented core that includes aninner core region surrounded by an outer core region, where the innercore region comprises updoped silica glass and has a positive maximumrelative refractive index Δ_(1max) and the outer core region comprisesdowndoped silica glass and has a negative minimum relative refractiveindex Δ_(1min). The updoped silica glass of the inner core regionincludes an updopant or a combination of an updopant and downdopant.

In embodiments in which the inner core region includes a combination anupdopant and downdopant, the relative concentrations of updopant anddowndopant may be adjusted to provide a net positive value of themaximum relative refractive index.

In embodiments in which the outer core region includes a combination anupdopant and downdopant, the relative concentrations of updopant anddowndopant may be adjusted to provide a net negative value of therelative refractive index.

In embodiments with a segmented core, Δ₁ (and Δ_(1max) and Δ_(1min))refer to the entirety of the core region, including the inner coreregion and the outer core region, r₁ corresponds to the outer radius ofthe outer core region, and r_(1a) corresponds to the outer radius of theinner core region. The boundary between the inner core region and outercore region occurs at radial position r_(1a), where r_(1a)<r₁.

In various embodiments, the outer radius r₁ of the core is in a rangefrom 2.0 μm to 20 μm, or in a range from 2.0 μm to 10 μm, or in a rangefrom 2.0 μm to 8.0 μm, or in a range from 3.0 μm to 7.0 μm, or in arange from 3.0 μm to 6.5 μm, or in a range from 3.0 μm to 6.0 μm, or ina range from 3.6 μm to 5.4 μm, or in a range from 4.0 μm to 5.0 μm, orin a range from 4.2 μm to 4.8 μm. In some embodiments, the relativerefractive index of the core is described by a step-index profile (e.g.α-profile with α≥10) having a constant or approximately constant valuecorresponding to Δ₁ in a range from 0.15% to 0.50%, or in a range from0.20% to 0.45%, or in a range from 0.25% to 0.50%, or in a range from0.25% to 0.40%, or in a range from 0.32% to 0.42%, or in a range from0.34% to 0.40%, or in a range from 0.35% to 0.39%. In some otherembodiments, the relative refractive index of the core is described by agraded-index profile (e.g. α-profile with α<10). The correspondingmaximum relative refractive index Δ_(1max) of the core region of thegraded-index profile is in a range from 0.15% to 0.50%, or in a rangefrom 0.20% to 0.45%, or in a range from 0.25% to 0.40%, or in a rangefrom 0.32% to 0.42%, or in a range from 0.34% to 0.40%, or in a rangefrom 0.35% to 0.39%.

Cores with a relative refractive index having or that can be modelled asan α-profile have values of a in a range from 1 to 200, or in a rangefrom 1 to 100, or in a range from 1 to 20, or in a range from 1 to 10,or in a range from 2 to 8, or in a range from 3 to 7, or in a range from5 to 15, or in a range from 7 to 13, or in a range from 6 to 12, or in arange from 10 to 100, or in a range from 20 to 100.

In some embodiments, a core volume V₁ of the core region is in a rangefrom 2.0%-μm² to 10.0%-μm², or in a range from 2.5%-μm² to 8.0%-μm², orin a range from 3.0%-μm² to 6.0%-μm², or in a range from 3.4%-μm² to4.4%-μm², or in a range from 3.0%-μm² to 4.6%-μm², in a range from5.8%-μm² to 6.8%-μm², or in a range from 6.0%-μm² to 6.6%-μm², or atleast 5.8%-μm², or at least 6.0%-μm², or at 6.2%-μm².

In some embodiments, the core can be doped with chlorine (“Cl-doped”hereinafter), with the chlorine concentration in a range from 1.5 wt %to 6.0 wt %, or in a range from 2.0 wt % to 5.5 wt %, or in a range from2.5 wt % to 5.0 wt %, or in a range from 3.0 wt % to 4.5 wt %, orgreater than or equal to 1.5 wt % (e.g., ≥2 wt %, ≥2.5 wt %, ≥3 wt %,≥3.5 wt %, ≥4 wt %, ≥4.5 wt %, ≥5 wt %, etc.) It is noted that, thenotation “wt %” used herein means a weight percentage. It is also notedthat, the core is GeO₂ free, or a concentration of GeO₂ in the cores isless than 1.0 wt %.

In various embodiments in which the cladding includes an inner claddingsurrounded by and directly adjacent to a depressed-index claddingregion. The outer radius r₂ of the inner cladding is greater than 8.0μm, or greater than 9.0 μm, or greater than 10.0 μm, or less than 12.0μm, or less than 11.0 μm, or less than 10.0 μm, or in a range from 8.0μm to 12.0 μm, or in a range from 9.0 μm to 11.0 μm. A thickness (r₂−r₁)of the inner cladding is in a range from 2.0 μm to 10.0 μm, or in arange from 3.0 μm to 9.0 μm, or in a range from 4.0 μm to 8.0 μm.

The relative refractive index Δ₂ of the inner cladding is in a rangefrom −0.15% to 0.15%, or in a range from −0.10% to 0.10%, or in a rangefrom −0.05 to 0.05%. In some embodiments, the inner cladding is a puresilica cladding. In some other embodiments, the inner cladding isdowndoped. For example, the inner cladding can be doped with fluorine(“F-doped” hereinafter) with a fluorine concentration in a range from0.01 wt % to 0.20 wt %, or in a range from 0.05 wt % to 0.15 wt %. Insome other embodiments, the inner cladding is updoped. For example, theinner cladding can be Cl-doped with a chlorine concentration in a rangefrom 0.01 wt % to 0.50 wt %, or in a range from 0.05 wt % to 0.40 wt %,or in a range from 0.10 wt % to 0.30 wt %.

In embodiments in which the cladding includes an inner cladding regionsurrounded by and directly adjacent to a depressed-index claddingregion, the inner radius of the depressed-index cladding region is r₂and has the values specified above. In various embodiments, the outerradius r₃ of the depressed-index cladding is less than 20 μm, or lessthan 18 μm, or less than 16 μm, or less than 15 μm, or greater than 10μm, or greater than 12 μm, or greater than 14 μm, or in a range from 10μm to 20 μm, or in a range from 12 μm to 18 μm. A thickness (r₃−r₂) ofthe depressed-index cladding is in a range from 3 μm to 10 μm, or in arange from 3.5 μm to 9 μm, or in a range from 4 μm to 8 μm, or in arange from 4.5 μm to 6.5 μm. The relative refractive index Δ₃ of thedepressed-index cladding is in a range from −0.8% to 0.0%, or in a rangefrom −0.7% to −0.1%, or in a range from −0.6% to −0.2%. As describedabove, the depressed-index cladding is downdoped, such as being F-dopedwith a fluorine concentration in a range from 0.10 wt % to 0.50 wt %, orin a range from 0.15 wt % to 0.45 wt %, or in a range from 0.20 wt % to0.40 wt %, or greater than 0.10 wt %, or greater than 0.15 wt %, orgreater than 0.20 wt %. A trench volume of the depressed-index claddingis greater than 20%-μm², or greater than 30%-μm², or greater than40%-μm², or greater than 50%-μm², or greater than 60%-μm², or in a rangefrom 20%-μm² to 70%-μm², or in a range from 20%-μm² to 80%-μm², or in arange from 30%-μm² to 70%-μm², or in a range from 30%-μm² to 60%-μm², orin a range from 20%-μm² to 100%-μm².

It is noted that, in some embodiments, the cladding includes only theinner cladding and outer cladding without the interveningdepressed-index cladding, as described above in connection with FIG. 7B.In such embodiments, the inner cladding surrounds and is directlyadjacent to the core and the first outer cladding surrounds and isdirectly adjacent to the inner cladding. In these embodiments, the innercladding functions as a trench region.

In embodiments in which the cladding lacks an interveningdepressed-index cladding and has a first outer cladding surrounding anddirectly adjacent to an inner cladding that surrounds and is directlyadjacent to a core region, the inner radius of the inner cladding is r₁with the values specified above. In various embodiments, the outerradius r₂ of the inner cladding is less than 30 μm, or less than 25 μm,or less than 20 μm, or less than 15 μm, or less than 10 μm, or less than5 μm, or greater than 5 μm, or greater than 10 μm, or greater than 12μm, or greater than 15 μm, or greater than 20 μm, or greater than 25 μm,or in a range from 3 μm to 30 μm, or in a range from 5 μm to 25 μm, orin a range from 7 μm to 20 μm, or in a range from 10 μm to 18 μm. Athickness (r₂−r₁) of the inner cladding is in a range from 3 μm to 30μm, or in a range from 3 μm to 20 μm, or in a range from 4 μm to 25 μm,or in a range from 4 μm to 18 μm, or in a range from 6 μm to 20 μm, orin a range from 6 μm to 15 μm, or in a range from 7 μm to 13 μm, or in arange from 8 μm to 15 μm. The relative refractive index Δ₂ of the innercladding is in a range from −0.8% to 0.0%, or in a range from −0.7% to−0.1%, or in a range from −0.6% to −0.2%. In these embodiments, theinner cladding is downdoped, such as being F-doped with a fluorineconcentration in a range from 0.10 wt % to 0.50 wt %, or in a range from0.15 wt % to 0.45 wt %, or in a range from 0.20 wt % to 0.40 wt %, orgreater than 0.10 wt %, or greater than 0.15 wt %, or greater than 0.20wt %. A trench volume of the inner cladding is greater than 20%-μm², orgreater than 30%-μm², or greater than 40%-μm², or greater than 50%-μm²,or greater than 60%-μm², or in a range from 20%-μm² to 70%-μm², or in arange from 20%-μm² to 80%-μm², or in a range from 30%-μm² to 70%-μm², orin a range from 30%-μm² to 60%-μm², or in a range from 20%-μm² to100%-μm², or in a range from 20%-μm² to 150%-μm², or in a range from20%-μm² to 200%-μm².

The inner radius of the first outer cladding region is r₃ (inembodiments in which the first outer cladding is directly adjacent to adepressed-index cladding that is directly adjacent to an inner claddingthat is directly adjacent to a core) or r₂ (in embodiments in which thefirst outer cladding is directly adjacent to an inner cladding that isdirectly adjacent to a core) and has the values specified above. Invarious embodiments, a thickness (r_(4a)−r₃) or (r_(4a)−r₂) of the firstouter cladding is in a range from 5 μm to 30 μm, or in a range from 7 μmto 28 μm, or in a range from 10 μm to 25 μm, or in a range from 12 μm to23 μm. The radius r_(4a) of the first outer cladding region is less thanor equal to 43 μm, or less than or equal to 40 μm, or less than or equalto 35 μm, or less than or equal to 30 μm, or less than or equal to 25μm, or in a range from 15 μm to 43 μm, or in a range from 22.5 μm to37.5 μm, or in a range from 25 μm to 35 μm, or in a range from 20 μm to43 μm, or in a range from 25 μm to 42 μm, or in a range from 30 μm to 40μm, or in a range from 32 μm to 38 μm. The relative refractive indexΔ_(4a) of the first outer cladding is in a range from −0.15% to 0.15%,or in a range from −0.10% to 0.10%, or in a range from −0.05 to 0.05%,or in a range from −0.15% to 0.0%, or in a range from −0.10% to 0.0%. Insome embodiments, the first outer cladding is a pure silica cladding. Insome other embodiments, the first outer cladding is downdoped. Forexample, the first outer cladding can be doped with fluorine (“F-doped”hereinafter) with a fluorine concentration in a range from 0.01 wt % to0.20 wt %, or in a range from 0.05 wt % to 0.15 wt %. In some otherembodiments, the first outer cladding is updoped. For example, the firstouter cladding can be Cl-doped with a chlorine concentration in a rangefrom 0.01 wt % to 0.50 wt %, or in a range from 0.05 wt % to 0.40 wt %,or in a range from 0.10 wt % to 0.30 wt %.

The inner radius of the second outer cladding region is r_(4a) and hasthe values specified above. In various embodiments, a thickness(r_(4b)−r_(4a)) of the second outer cladding is in a range from 2 μm to30 μm, or in a range from 2 μm to 25 μm, or in a range from 2 μm to 20μm, or in a range from 2 μm to 15 μm, or in a range from 2 μm to 10 μmor in a range from 5 μm to 25 μm, or in a range from 6 μm to 20 μm, orin a range from 8 μm to 17 μm, or in a range from 10 μm to 15 μm. Invarious embodiments, the outer radius r_(4b) of the second outercladding is less than or equal to 45 μm, or less than or equal to 42.5μm, or less than or equal to 40 μm, or less than or equal to 37.5 μm, orless than or equal to 35 μm, or in a range from 20 μm to 45 μm, or in arange from 25 μm to 45 μm, or in a range from 25 μm to 42.5 μm, or in arange from 25 μm to 40 μm, or in a range from 27.5 μm to 45 μm, or in arange from 27.5 μm to 42.5 μm, or in a range from 27.5 μm to 40 μm, orin a range from 30 μm to 45 μm, or in a range from 30 μm to 42.5 μm, orin a range from 30 μm to 40 μm, or in a range from 32.5 μm to 45 μm, orin a range from 32.5 μm to 42.5 μm, or in a range from 32.5 μm to 40 μm.The relative refractive index Δ_(4b) of the second outer cladding is ina range from 0.2% to 2%, or in a range from 0.4% to 1.8%, or in a rangefrom 0.6% to 1.6%, or in a range from 0.8% to 1.4%, or in a range from0.9% to 1.2%. In some embodiments, the relative refractive index Δ_(4b)of the second outer cladding is greater than the maximum relativerefractive index Δ_(1max) of the core region. In some other embodiments,the second outer cladding is updoped. For example, the second outercladding can be doped with a titania (TiO₂) concentration in a rangefrom 1 wt % to 20 wt %, or in a range from 4 wt % to 20 wt %, or in arange from 6 wt % to 15 wt %, or in a range from 8 wt % to 12 wt %.

The mode field diameter of the single mode optical fibers disclosedherein is greater than or equal to 8.2 μm, or greater than or equal to8.4 μm, or greater than or equal to 8.6 μm, or greater than or equal to8.8 μm, or less than or equal to 9.8 μm, or less than or equal to 9.6μm, or less than or equal to 9.4 μm, or less than or equal to 9.2 μm, orin a range from 8.2 μm to 9.8 μm, or in a range from 8.3 μm to 9.6 μm,or in a range from 8.4 μm to 9.5 μm, or in a range from 8.3 μm to 9.4 μmat a wavelength of 1310 nm.

The mode field diameter of the single mode optical fibers disclosedherein is greater than or equal to 9.0 μm, or greater than or equal to9.2 μm, or greater than or equal to 9.4 μm, or than or equal to 9.6 μm,or greater than or equal to 9.8 μm, or less than or equal to 11.0 μm, orless than or equal to 10.8 μm, or less than or equal to 10.6 μm, or lessthan or equal to 10.4 μm, or in a range from 9.0 μm to 11.0 μm, or in arange from 9.1 μm to 10.8 μm, or in a range from 9.2 μm to 10.6 μm, orin a range from 9.3 μm to 10.4 μm at a wavelength of 1550 nm.

The effective area A_(eff) of the single mode optical fibers disclosedherein is greater than 50 μm², or greater than 55 μm², or greater than60 μm², or greater than 65 μm², or greater than 70 μm², or less than 130μm², or less than 115 μm², or less than 100 μm², or in the range from 50μm² to 100 μm², or in the range from 55 μm² to 90 μm², or in the rangefrom 60 μm² to 80 μm² at a wavelength of 1310 nm.

The effective area A_(eff) of the single mode optical fibers disclosedherein is greater than 100 μm², or greater than 110 μm², or greater than120 μm², or greater than 130 μm², or greater than 140 μm², or greaterthan 150 μm², or in the range from 100 μm² to 180 μm², or in the rangefrom 110 μm² to 165 μm², or in the range from 120 μm² to 155 μm² at awavelength of 1550 nm.

The attenuation of the single mode optical fibers disclosed herein isless than or equal to 0.170 dB/km, or less than or equal to 0.165 dB/km,or less than or equal to 0.160 dB/km, or less than or equal to 0.155dB/km, or less than or equal to 0.150 dB/km at a wavelength of 1550 nm.

It is noted that, macrobending loss can be determined using a mandrelwrap test specified in standard IEC 60793-1-47. In the mandrel wraptest, the optical fiber is wrapped one or more times around acylindrical mandrel having a specified diameter, and the increase inattenuation at a specified wavelength due to the bending is determined.Attenuation in the mandrel wrap test is expressed in units of dB/turn,where one turn refers to one revolution of the optical fiber about themandrel. Macrobending losses at a wavelength of 1310 nm or 1550 nm weredetermined for selected examples described below with the mandrel wraptest using mandrels with diameters of ranging from 10 mm to 60 mm. Insome embodiments, the bending loss of the optical fibers at a wavelengthof 1310 nm as determined by the mandrel wrap test using a mandrel havinga diameter of 15 mm can be less than 3.0 dB/turn, or less than 2.5dB/turn, or less than 2.0 dB/turn, or less than 1.5 dB/turn, or lessthan 1.0 dB/turn. In some embodiments, the bending loss of the opticalfibers at a wavelength of 1550 nm as determined by the mandrel wrap testusing a mandrel having a diameter of 10 mm can be less than 3.0 dB/turn,or less than 2.5 dB/turn, or less than 2.0 dB/turn, or less than 1.5dB/turn, or less than 1.0 dB/turn.

In some embodiments, the fiber cutoff wavelength λ_(CF) of the opticalfibers disclosed herein is less than 1530 nm, or less than 1520 nm, orless than 1500 nm, or less than 1450 nm, or less than 1400 nm, or lessthan 1350 nm, or less than 1300 nm, or less than 1260 nm or less than1210 nm, or less than 1160 nm, or less than 1110 nm, or less than 1060nm. The cable cutoff λ_(CC) of the optical fibers disclosed herein isless than 1530 nm, or less than 1520 nm, or less than 1500 nm, or lessthan 1450 nm, or less than 1400 nm, or less than 1350 nm, less than 1300nm, or less than 1260 nm, or less than 1210 nm, or less than 1160 nm, orless than 1110 nm, or less than 1060 nm.

In some embodiments, the zero dispersion wavelength (λ₀) of the singlemode optical fibers disclosed herein is in a range 1200 nm to 1500 nm,in a range 1240 nm to 1400 nm, or in a range 1280 nm to 1360 nm, or in arange 1300 nm to 1324 nm.

In some embodiments, the overfilled launch (OFL) bandwidth of the singlemode optical fibers disclosed herein is greater than 200 MHz-km(e.g., >300 MHz-km, >400 MHz-km, >500 MHz-km, greater than 1000 MHz-km,greater than 2000 MHz-km, greater than 4000 MHz-km, etc.) at awavelength of 850 nm, 980 nm, 1064 nm, and/or 1300 nm (that is, theoverfilled launch (OFL) bandwidth has the value specified at at leastone of the wavelengths of 850 nm, 980 nm, 1064 nm, and 1300 nm).

In some embodiments, the puncture resistance of the secondary coating ofthe single mode optical fibers disclosed herein can be greater than 30 g(e.g., >40 g, >50 g, etc.). In some embodiments, the normalized punctureload of the optical fiber 100 is greater than 3.6×10⁻³ g/μm² (e.g.,>3.8×10⁻³ g/μm², >4.0×10⁻³ g/μm², etc.).

In some embodiments, proper combination of the fiber parameters in theranges described above can result in optical fiber properties that meetthe requirements of a high transmission capacity, a small diameter, alow transmission loss, good microbending properties, and high punctureresistance. The profiles designs shown in FIGS. 7A to 7E, other profilesas described herein, and the various fiber parameters described abovecan be compliant with various optical fibers, such as ITU G.652.D,G.657.A1, G.657.A2, G.654, etc.

Optical Fiber Coatings

The transmissivity of light through an optical fiber is highly dependenton the properties of the coatings applied to the glass fiber. Thecoatings typically include a primary coating and a secondary coating,where the secondary coating surrounds the primary coating and theprimary coating contacts the glass fiber (which includes a central coreregion surrounded by a cladding region). The secondary coating is aharder material (higher in situ modulus) than the primary coating and isdesigned to protect the glass fiber from damage caused by abrasion orexternal forces that arise during processing, handling, and installationof the optical fiber. The primary coating is a softer material (lower insitu modulus) than the secondary coating and is designed to buffer ordissipates stresses that result from lateral forces applied to the outersurface of the secondary coating. The primary coating is especiallyimportant in dissipating stresses that arise due to the microbends thatthe optical fiber encounters when deployed in a cable. The primarycoating should maintain adequate adhesion to the glass fiber duringthermal and hydrolytic aging, yet be strippable from the glass fiber forsplicing purposes.

Primary and secondary coatings are typically formed by applying acurable coating composition to the glass fiber as a viscous liquid andcuring. The optical fiber may also include a tertiary coating (notshown) that surrounds the secondary coating. The tertiary coating mayinclude pigments, inks or other coloring agents to mark the opticalfiber for identification purposes and typically has an in situ modulussimilar to the in situ modulus of the secondary coating.

As described above, the design of the refractive index profile of thecladding may include a refractive index trench that diminishes thesensitivity of the coated fiber to bending, and a titania-doped outercladding, which improves the mechanical reliability of the fiber andprovides a substantial increase in resistance to mechanical abrasion.This cladding structure may enable use of a primary coating and asecondary coating with reduced thickness relative to commerciallyavailable fibers. The thinner coating thickness of the optical fiberembodiments described herein advantageously provides compact coatedfibers that can be densely packed and/or readily installed in existingfiber infrastructures. The mechanical properties of the primary coatingare selected such that good microbending performance of the coated fiberis achieved, even when the thickness of the primary coating is reduced.The mechanical properties of the secondary coating are selected suchthat good puncture resistance of the coated fiber is achieved, even whenthe thickness of the secondary coating is reduced.

Primary Coating—Compositions. The primary coating is a cured product ofa curable primary coating composition. The curable primary coatingcompositions provide a primary coating for optical fibers that exhibitslow Young's modulus, low pullout force, and strong cohesion. The curableprimary coating compositions further enable formation of a primarycoating that features clean strippability and high resistance to defectformation during the stripping operation. Low pullout force facilitatesclean stripping of the primary coating with minimal residue and strongcohesion inhibits initiation and propagation of defects in the primarycoating when it is subjected to stripping forces. Even for opticalfibers with reduced primary coating thicknesses, the optical fibers areexpected to have low loss and low microbend loss performance. Theprimary coatings exhibit these advantages even at reduced thickness.

The primary coating is a cured product of a radiation-curable primarycoating composition that includes an oligomer, a monomer, aphotoinitiator and, optionally, an additive. The following disclosuredescribes oligomers for the radiation-curable primary coatingcompositions, radiation-curable primary coating compositions containingat least one of the oligomers, cured products of the radiation-curableprimary coating compositions that include at least one of the oligomers,glass fibers coated with a radiation-curable primary coating compositioncontaining at least one of the oligomers, and glass fibers coated withthe cured product of a radiation-curable primary coating compositioncontaining at least one of the oligomers.

The oligomer preferably includes a polyether urethane diacrylatecompound and a di-adduct compound. In one embodiment, the polyetherurethane diacrylate compound has a linear molecular structure. In oneembodiment, the oligomer is formed from a reaction between adiisocyanate compound, a polyol compound, and a hydroxy acrylatecompound, where the reaction produces a polyether urethane diacrylatecompound as a primary product (majority product) and a di-adductcompound as a byproduct (minority product). The reaction forms aurethane linkage upon reaction of an isocyanate group of thediisocyanate compound and an alcohol group of the polyol. The hydroxyacrylate compound reacts to quench residual isocyanate groups that arepresent in the composition formed from reaction of the diisocyanatecompound and polyol compound. As used herein, the term “quench” refersto conversion of isocyanate groups through a chemical reaction withhydroxyl groups of the hydroxy acrylate compound. Quenching of residualisocyanate groups with a hydroxy acrylate compound converts terminalisocyanate groups to terminal acrylate groups.

A preferred diisocyanate compound is represented by formula (I):O═C═N—R₁—N═C═O  (I)which includes two terminal isocyanate groups separated by a linkagegroup R₁. In one embodiment, the linkage group R₁ includes an alkylenegroup. The alkylene group of linkage group R₁ is linear (e.g. methyleneor ethylene), branched (e.g. isopropylene), or cyclic (e.g.cyclohexylene, phenylene). The cyclic group is aromatic or non-aromatic.In some embodiments, the linkage group R₁ is 4,4′-methylenebis(cyclohexyl) group and the diisocyanate compound is 4,4′-methylenebis(cyclohexyl isocyanate). In some embodiments, the linkage group R₁lacks an aromatic group, or lacks a phenylene group, or lacks anoxyphenylene group.

The polyol is represented by molecular formula (II):

where R₂ includes an alkylene group, O—R₂— is a repeating alkoxylenegroup, and x is an integer. Preferably, x is greater than 20, or greaterthan 40, or greater than 50, or greater than 75, or greater than 100, orgreater than 125, or greater than 150, or in the range from 20 to 500,or in the range from 20 to 300, or in the range from 30 to 250, or inthe range from 40 to 200, or in the range from 60 to 180, or in therange from 70 to 160, or in the range from 80 to 140. R₂ is preferably alinear or branched alkylene group, such as methylene, ethylene,propylene (normal, iso or a combination thereof), or butylene (normal,iso, secondary, tertiary, or a combination thereof). The polyol may be apolyalkylene oxide, such as polyethylene oxide, or a polyalkyleneglycol, such as polypropylene glycol. Polypropylene glycol is apreferred polyol. The molecular weight of the polyol is greater than1000 g/mol, or greater than 2500 g/mol, or greater than 5000 g/mol, orgreater than 7500 g/mol, or greater than 10000 g/mol, or in the rangefrom 1000 g/mol to 20000 g/mol, or in the range from 2000 g/mol to 15000g/mol, or in the range from 2500 g/mol to 12500 g/mol, or in the rangefrom 2500 g/mol to 10000 g/mol, or in the range from 3000 g/mol to 7500g/mol, or in the range from 3000 g/mol to 6000 g/mol, or in the rangefrom 3500 g/mol to 5500 g/mol. In some embodiments, the polyol ispolydisperse and includes molecules spanning a range of molecularweights such that the totality of molecules combines to provide thenumber average molecular weight specified hereinabove.

The unsaturation of the polyol is less than 0.25 meq/g, or less than0.15 meq/g, or less than 0.10 meq/g, or less than 0.08 meq/g, or lessthan 0.06 meq/g, or less than 0.04 meq/g, or less than 0.02 meq/g, orless than 0.01 meq/g, or less than 0.005 meq/g, or in the range from0.001 meq/g to 0.15 meq/g, or in the range from 0.005 meq/g to 0.10meq/g, or in the range from 0.01 meq/g to 0.10 meq/g, or in the rangefrom 0.01 meq/g to 0.05 meq/g, or in the range from 0.02 meq/g to 0.10meq/g, or in the range from 0.02 meq/g to 0.05 meq/g. As used herein,unsaturation refers to the value determined by the standard methodreported in ASTM D4671-16. In the method, the polyol is reacted withmercuric acetate and methanol in a methanolic solution to produceacetoxymercuricmethoxy compounds and acetic acid. The reaction of thepolyol with mercuric acetate is equimolar and the amount of acetic acidreleased is determined by titration with alcoholic potassium hydroxideto provide the measure of unsaturation used herein. To preventinterference of excess mercuric acetate on the titration of acetic acid,sodium bromide is added to convert mercuric acetate to the bromide.

The reaction to form the oligomer further includes addition of a hydroxyacrylate compound to react with terminal isocyanate groups present inunreacted starting materials (e.g. the diisocyanate compound) orproducts formed in the reaction of the diisocyanate compound with thepolyol (e.g. urethane compounds with terminal isocyanate groups). Thehydroxy acrylate compound reacts with terminal isocyanate groups toprovide terminal acrylate groups for one or more constituents of theoligomer. In some embodiments, the hydroxy acrylate compound is presentin excess of the amount needed to fully convert terminal isocyanategroups to terminal acrylate groups. The oligomer includes a singlepolyether urethane acrylate compound or a combination of two or morepolyether urethane acrylate compounds.

The hydroxy acrylate compound is represented by molecular formula (III):

where R₃ includes an alkylene group. The alkylene group of R₃ is linear(e.g. methylene or ethylene), branched (e.g. isopropylene), or cyclic(e.g. phenylene). In some embodiments, the hydroxy acrylate compoundincludes substitution of the ethylenically unsaturated group of theacrylate group. Substituents of the ethylenically unsaturated groupinclude alkyl groups. An example of a hydroxy acrylate compound with asubstituted ethylenically unsaturated group is a hydroxy methacrylatecompound. The discussion that follows describes hydroxy acrylatecompounds. It should be understood, however, that the discussion appliesto substituted hydroxy acrylate compounds and in particular to hydroxymethacrylate compounds.

In different embodiments, the hydroxy acrylate compound is ahydroxyalkyl acrylate, such as 2-hydroxyethyl acrylate

In the foregoing exemplary molecular formulas (I), II), and (III), thegroups R₁, R₂, and R₃ independently are all the same, are all different,or include two groups that are the same and one group that is different.

The diisocyanate compound, hydroxy acrylate compound and polyol arecombined simultaneously and reacted, or are combined sequentially (inany order) and reacted. In one embodiment, the oligomer is formed byreacting a diisocyanate compound with a hydroxy acrylate compound andreacting the resulting product composition with a polyol. In anotherembodiment, the oligomer is formed by reacting a diisocyanate compoundwith a polyol compound and reacting the resulting product compositionwith a hydroxy acrylate compound.

The oligomer is formed from a reaction of a diisocyanate compound, ahydroxy acrylate compound, and a polyol, where the molar ratio of thediisocyanate compound to the hydroxy acrylate compound to the polyol inthe reaction process is n:m:p. n, m, and p are referred to herein asmole numbers or molar proportions of diisocyanate, hydroxy acrylate, andpolyol; respectively. The mole numbers n, m and p are positive integeror positive non-integer numbers. In embodiments, when p is 2.0, n is inthe range from 3.0 to 5.0, or in the range from 3.2 to 4.8, or in therange from 3.4 to 4.6, or in the range from 3.5 to 4.4, or in the rangefrom 3.6 to 4.2, or in the range from 3.7 to 4.0; and m is in the rangefrom 1.5 to 4.0, or in the range from 1.6 to 3.6, or in the range from1.7 to 3.2, or in the range from 1.8 to 2.8, or in the range from 1.9 to2.4. For values of p other than 2.0, the molar ratio n:m:p scalesproportionally. For example, the molar ratio n:m:p=4.0:3.0:2.0 isequivalent to the molar ratio n:m:p=2.0:1.5:1.0.

In one embodiment, the oligomer is formed from a reaction mixture thatincludes 4,4′-methylene bis(cyclohexyl isocyanate), 2-hydroxyethylacrylate, and polypropylene glycol in the molar ratios n:m:p asspecified above, where the polypropylene glycol has a number averagemolecular weight in the range from 2500 g/mol to 6500 g/mol, or in therange from 3000 g/mol to 6000 g/mol, or in the range from 3500 g/mol to5500 g/mol.

The oligomer preferably includes two components. The first component isa polyether urethane diacrylate compound having the molecular formula(IV):

and the second component is a di-adduct compound having the molecularformula (V):

where the groups R₁, R₂, R₃, and the integer x are as describedhereinabove, y is a positive integer, and it is understood that thegroup R₁ in molecular formulas (IV) and (V) is the same as group R₁ inmolecular formula (I), the group R₂ in molecular formula (IV) is thesame as group R₂ in molecular formula (II), and the group R₃ inmolecular formulas (IV) and (V) is the same as group R₃ in molecularformula (III). The di-adduct compound corresponds to the compound formedby reaction of both terminal isocyanate groups of the diisocyanatecompound of molecular formula (I) with the hydroxy acrylate compound ofmolecular formula (II) where the diisocyanate compound has undergone noreaction with the polyol of molecular formula (II).

The di-adduct compound is formed from a reaction of the diisocyanatecompound with the hydroxy acrylate compound during the reaction used toform the oligomer. Alternatively, the di-adduct compound is formedindependent of the reaction used to form the oligomer and is added tothe product of the reaction used to form the polyether urethanediacrylate compound or to a purified form of the polyether urethanediacrylate compound. The hydroxy group of the hydroxy acrylate compoundreacts with an isocyanate group of the diisocyanate compound to providea terminal acrylate group. The reaction occurs at each isocyanate groupof the diisocyanate compound to form the di-adduct compound. Thedi-adduct compound is present in the oligomer in an amount of at least1.0 wt %, or at least 1.5 wt %, or at least 2.0 wt %, or at least 2.25wt %, or at least 2.5 wt %, or at least 3.0 wt %, or at least 3.5 wt %,or at least 4.0 wt %, or at least 4.5 wt %, or at least 5.0 wt %, or atleast 7.0 wt % or at least 9.0 wt %, or in the range from 1.0 wt % to10.0 wt %, or in the range from 2.0 wt % to 9.0 wt %, or in the rangefrom 2.5 wt % to 6.0 wt %, or in the range from 3.0 wt % to 8.0 wt %, orin the range from 3.0 wt % to 5.0 wt %, or in the range from 3.0 wt % to5.5 wt %, or in the range from 3.5 wt % to 5.0 wt %, or in the rangefrom 3.5 wt % to 7.0 wt %. It is noted that the concentration ofdi-adduct is expressed in terms of wt % of the oligomer and not in termsof wt % in the coating composition.

An illustrative reaction for synthesizing an oligomer in accordance withthe present disclosure includes reaction of a diisocyanate compound(4,4′-methylene bis(cyclohexyl isocyanate, which is also referred toherein as H12MDI) and a polyol (polypropylene glycol with M_(n)˜4000g/mol, which is also referred to herein as PPG4000) to form a polyetherurethane diisocyanate compound with formula (VI):H12MDI˜PPG4000˜H12MDI˜PPG4000˜H12MDI  (VI)where “˜” denotes a urethane linkage formed by the reaction of aterminal isocyanate group of H12MDI with a terminal alcohol group ofPPG4000; and ˜H12MDI, ˜H12MDI˜, and ˜PPG4000˜ refer to residues ofH12MDI and PPG4000 remaining after the reaction; and M_(n) refers tonumber average molecular weight. The polyether urethane diisocyanatecompound has a repeat unit of the type˜(H12MDI˜PPG4000)˜. The particularpolyether urethane diisocyanate shown includes two PPG4000 units. Thereaction may also provide products having one PPG4000 unit, or three ormore PPG4000 units. The polyether urethane diisocyanate and anyunreacted H12MDI include terminal isocyanate groups. In accordance withthe present disclosure, a hydroxy acrylate compound (such as2-hydroxyethyl acrylate, which is referred to herein as HEA) is includedin the reaction to react with terminal isocyanate groups to convert themto terminal acrylate groups. The conversion of terminal isocyanategroups to terminal acrylate groups effects a quenching of the isocyanategroup. The amount of HEA included in the reaction may be an amountestimated to react stoichiometrically with the expected concentration ofunreacted isocyanate groups or an amount in excess of the expectedstoichiometric amount. Reaction of HEA with the polyether urethanediisocyanate compound forms the polyether urethane acrylate compoundwith formula (VII):HEA˜H12MDI˜PPG4000˜H12MDI˜PPG4000˜H12MDI  (VII)and/or the polyether urethane diacrylate compound with formula (VIII):HEA˜H12MDI˜PPG4000˜H12MDI˜PPG4000˜H12MDI˜HEA  (VIII)and reaction of HEA with unreacted H12MDI forms the di-adduct compoundwith formula (IX):HEA˜H12MDI˜HEA  (IX)where, as above, ˜ designates a urethane linkage and ˜HEA designates theresidue of HEA remaining after reaction to form the urethane linkage(consistent with formulas (IV) and (V)). The combination of a polyetherurethane diacrylate compound and a di-adduct compound in the productcomposition constitutes an oligomer in accordance with the presentdisclosure. As described more fully hereinbelow, when one or moreoligomers are used in coating compositions, coatings having improvedtear strength and critical stress characteristics result. In particular,it is demonstrated that oligomers having a high proportion of di-adductcompound provide coatings with high tear strengths and/or high criticalstress values.

The oligomer includes a compound that is a polyether urethane diacrylatecompound with formula (X):(hydroxy acrylate)˜(diisocyanate˜polyol)_(x)˜diisocyanate˜(hydroxyacrylate)  (X)and a compound that is a di-adduct compound with formula (XI):(hydroxy acrylate)˜diisocyanate˜(hydroxy acrylate)  (XI)where the relative proportions of diisocyanate compound, hydroxyacrylate compound, and polyol used in the reaction to form the oligomercorrespond to the mole numbers n, m, and p disclosed hereinabove.

Compounds represented by molecular formulas (I) and (II) above, forexample, react to form a polyether urethane diisocyanate compoundrepresented by molecular formula (XII):

where y is the same as y in formula (IV) and is 1, or 2, or 3 or 4 orhigher; and x is determined by the number of repeat units of the polyol(as described hereinabove).

Further reaction of the polyether urethane isocyanate of molecularformula (VI) with the hydroxy acrylate of molecular formula (III)provides the polyether urethane diacrylate compound represented bymolecular formula (IV) referred to hereinabove and repeated below:

where y is 1, or 2, or 3, or 4 or higher; and x is determined by thenumber of repeat units of the polyol (as described hereinabove).

Variations in the mole numbers n, m, and p provide control over therelative proportions of polyether urethane diacrylate and di-adductformed in the reaction. Increasing the mole number n relative to themole number m or the mole number p, for example, may increase the amountof di-adduct compound formed in the reaction. Reaction of thediisocyanate compound, the hydroxy acrylate compound, and polyolcompound in molar ratios n:m:p, where n is in the range from 3.0 to 5.0,m is in the range within ±15% of 2n−4 or within ±10% of 2n−4 orwithin±5% of 2n−4, and p is 2.0, for example, produce amounts of thedi-adduct compound in the oligomer sufficient to achieve the preferredprimary coating properties. By way of example, the embodiment in whichn=4.0, m is within ±15% of 2n−4, and p=2.0 means that n=4.0, m is within±15% of 4, and p=2.0, which means that that n=4.0, m is in the rangefrom 3.4 to 4.6, and p=2.0.

Variations in the relative proportions of di-adduct and polyetherurethane diacrylate are obtained through changes in the mole numbers n,m, and p and through such variations, it is possible to preciselycontrol the Young's modulus, in situ modulus, tear strength, criticalstress, tensile toughness, and other mechanical properties of coatingsformed from coating compositions that include the oligomer.

Improved fiber primary coatings result when utilizing a primary coatingcomposition that incorporates an oligomer that includes a polyetherurethane acrylate compound represented by molecular formula (IV) and adi-adduct compound represented by molecular formula (V), whereconcentration of the di-adduct compound in the oligomer is at least 1.0wt %, or at least 1.5 wt %, or at least 2.0 wt %, or at least 2.25 wt %,or at least 2.5 wt %, or at least 3.0 wt %, or at least 3.5 wt %, or atleast 4.0 wt %, or at least 4.5 wt %, or at least 5.0 wt %, or at least7.0 wt % or at least 9.0 wt %, or in the range from 1.0 wt % to 10.0 wt%, or in the range from 2.0 wt % to 9.0 wt %, or in the range from 3.0wt % to 8.0 wt %, or in the range from 3.5 wt % to 7.0 wt % or in therange from 2.5 wt % to 6.0 wt %, or in the range from 3.0 wt % to 5.5 wt%, or in the range from 3.5 wt % to 5.0 wt %. It is noted that theconcentration of di-adduct is expressed in terms of wt % of the oligomerand not in terms of wt % in the coating composition. The concentrationof the di-adduct compound is increased in one embodiment by varying themolar ratio n:m:p of diisocyanate:hydroxy acrylate:polyol. In oneaspect, molar ratios n:m:p that are rich in diisocyanate relative topolyol promote the formation of the di-adduct compound.

The oligomer of the primary coating composition includes a polyetherurethane diacrylate compound and di-adduct compound as describedhereinabove. In some embodiments, the oligomer includes two or morepolyether urethane diacrylate compounds and/or two or more di-adductcompounds. The oligomer content of the primary coating compositionincludes the combined amounts of the one or more polyether urethanediacrylate compound(s) and one or more di-adduct compound(s) and isgreater than 20 wt %, or greater than 30 wt %, or greater than 40 wt %,or in the range from 20 wt % to 80 wt %, or in the range from 30 wt % to70 wt %, or in the range from 40 wt % to 60 wt %, where theconcentration of di-adduct compound within the oligomer content is asdescribed above.

The curable primary coating composition further includes one or moremonomers. The one or more monomers is/are selected to be compatible withthe oligomer, to control the viscosity of the primary coatingcomposition to facilitate processing, and/or to influence the physicalor chemical properties of the coating formed as the cured product of theprimary coating composition. The monomers include radiation-curablemonomers such as ethylenically-unsaturated compounds, ethoxylatedacrylates, ethoxylated alkylphenol monoacrylates, propylene oxideacrylates, n-propylene oxide acrylates, isopropylene oxide acrylates,monofunctional acrylates, monofunctional aliphatic epoxy acrylates,multifunctional acrylates, multifunctional aliphatic epoxy acrylates,and combinations thereof.

Representative radiation-curable ethylenically unsaturated monomersinclude alkoxylated monomers with one or more acrylate or methacrylategroups. An alkoxylated monomer is one that includes one or morealkoxylene groups, where an alkoxylene group has the form —O—R— and R isa linear or branched alkylene group. Examples of alkoxylene groupsinclude ethoxylene (—O—CH₂—CH₂—), n-propoxylene (—O—CH₂—CH₂—CH₂—),isopropoxylene (—O—CH₂—CH(CH₃)—, or —O—CH(CH₃)—CH₂—), etc. As usedherein, the degree of alkoxylation refers to the number of alkoxylenegroups in the monomer. In one embodiment, the alkoxylene groups arebonded consecutively in the monomer.

In some embodiments, the primary coating composition includes analkoxylated monomer of the form R₄—R₅—O—(CH(CH₃)CH₂—O)_(q)—C(O)CH═CH₂,where R₄ and R₅ are aliphatic, aromatic, or a mixture of both, and q=1to 10, or R₄—O—(CH(CH₃)CH₂—O)_(q)—C(O)CH═CH₂, where C(O) is a carbonylgroup, R₁ is aliphatic or aromatic, and q=1 to 10.

Representative examples of monomers include ethylenically unsaturatedmonomers such as lauryl acrylate (e.g., SR335 available from SartomerCompany, Inc., AGEFLEX FA12 available from BASF, and PHOTOMER 4812available from IGM Resins), ethoxylated nonylphenol acrylate (e.g.,SR504 available from Sartomer Company, Inc. and PHOTOMER 4066 availablefrom IGM Resins), caprolactone acrylate (e.g., SR495 available fromSartomer Company, Inc., and TONE M-100 available from Dow Chemical),phenoxyethyl acrylate (e.g., SR339 available from Sartomer Company,Inc., AGEFLEX PEA available from BASF, and PHOTOMER 4035 available fromIGM Resins), isooctyl acrylate (e.g., SR440 available from SartomerCompany, Inc. and AGEFLEX FA8 available from BASF), tridecyl acrylate(e.g., SR489 available from Sartomer Company, Inc.), isobornyl acrylate(e.g., SR506 available from Sartomer Company, Inc. and AGEFLEX IBOAavailable from CPS Chemical Co.), tetrahydrofurfuryl acrylate (e.g.,SR285 available from Sartomer Company, Inc.), stearyl acrylate (e.g.,SR257 available from Sartomer Company, Inc.), isodecyl acrylate (e.g.,SR395 available from Sartomer Company, Inc. and AGEFLEX FA10 availablefrom BASF), 2-(2-ethoxyethoxy)ethyl acrylate (e.g., SR256 available fromSartomer Company, Inc.), epoxy acrylate (e.g., CN120, available fromSartomer Company, and EBECRYL 3201 and 3604, available from CytecIndustries Inc.), lauryloxyglycidyl acrylate (e.g., CN130 available fromSartomer Company) and phenoxyglycidyl acrylate (e.g., CN131 availablefrom Sartomer Company) and combinations thereof.

In some embodiments, the monomer component of the primary coatingcomposition includes a multifunctional (meth)acrylate. Multifunctionalethylenically unsaturated monomers include multifunctional acrylatemonomers and multifunctional methacrylate monomers. Multifunctionalacrylates are acrylates having two or more polymerizable acrylatemoieties per molecule, or three or more polymerizable acrylate moietiesper molecule. Examples of multifunctional (meth)acrylates includedipentaerythritol monohydroxy pentaacrylate (e.g., PHOTOMER 4399available from IGM Resins); methylolpropane polyacrylates with andwithout alkoxylation such as trimethylolpropane triacrylate,ditrimethylolpropane tetraacrylate (e.g., PHOTOMER 4355, IGM Resins);alkoxylated glyceryl triacrylates such as propoxylated glyceryltriacrylate with propoxylation being 3 or greater (e.g., PHOTOMER 4096,IGM Resins); and erythritol polyacrylates with and without alkoxylation,such as pentaerythritol tetraacrylate (e.g., SR295, available fromSartomer Company, Inc. (Westchester, Pa.)), ethoxylated pentaerythritoltetraacrylate (e.g., SR494, Sartomer Company, Inc.), dipentaerythritolpentaacrylate (e.g., PHOTOMER 4399, IGM Resins, and SR399, SartomerCompany, Inc.), tripropyleneglycol diacrylate, propoxylated hexanedioldiacrylate, tetrapropyleneglycol diacrylate, pentapropyleneglycoldiacrylate, methacrylate analogs of the foregoing, and combinationsthereof.

In some embodiments, the primary coating composition includes an N-vinylamide monomer such as an N-vinyl lactam, or N-vinyl pyrrolidinone, orN-vinyl caprolactam, where the N-vinyl amide monomer is present in thecoating composition at a concentration greater than 1.0 wt %, or greaterthan 2.0 wt %, or greater than 3.0 wt %, or in the range from 1.0 wt %to 15.0 wt %, or in the range from 2.0 wt % to 10.0 wt %, or in therange from 3.0 wt % to 8.0 wt %.

In an embodiment, the primary coating composition includes one or moremonofunctional acrylate or methacrylate monomers in an amount from 15 wt% to 90 wt %, or from 30 wt % to 75 wt %, or from 40 wt % to 65 wt %. Inanother embodiment, the primary coating composition may include one ormore monofunctional aliphatic epoxy acrylate or methacrylate monomers inan amount from 5 wt % to 40 wt %, or from 10 wt % to 30 wt %.

In different embodiments, the total monomer content of the primarycoating composition is between about 15 wt % and about 90 wt %, orbetween about 30 wt % and about 75 wt %, or between about 40 wt % andabout 65 wt %.

In addition to a curable monomer and a curable oligomer, the curableprimary coating composition also includes a polymerization initiator.The polymerization initiator facilitates initiation of thepolymerization process associated with the curing of the coatingcomposition to form the coating. Polymerization initiators includethermal initiators, chemical initiators, electron beam initiators, andphotoinitiators. Photoinitiators include ketonic photoinitiators and/orphosphine oxide photoinitiators.

Representative photoinitiators include 1-hydroxycyclohexylphenyl ketone(e.g., IRGACURE 184 available from BASF));bis(2,6-dimethoxybenzoyl)-2,4,4-trimethylpentylphosphine oxide (e.g.,commercial blends IRGACURE 1800, 1850, and 1700 available from BASF);2,2-dimethoxy-2-phenylacetophenone (e.g., IRGACURE 651, available fromBASF); bis(2,4,6-trimethylbenzoyl)-phenylphosphine oxide (IRGACURE 819);(2,4,6-trimethylbenzoyl)diphenyl phosphine oxide (LUCIRIN TPO, availablefrom BASF (Munich, Germany));ethoxy(2,4,6-trimethylbenzoyl)-phenylphosphine oxide (LUCIRIN TPO-L fromBASF); and combinations thereof.

The coating composition includes a single photoinitiator or acombination of two or more photoinitiators. The total photoinitiatorcontent of the coating composition is up to about 10 wt %, or betweenabout 0.5 wt % and about 6 wt %.

The curable primary coating composition optionally includes one or moreadditives. Additives include an adhesion promoter, a strength additive,an antioxidant, a catalyst, a stabilizer, an optical brightener, aproperty-enhancing additive, an amine synergist, a wax, a lubricant,and/or a slip agent.

An adhesion promoter is a compound that facilitates adhesion of theprimary coating and/or primary composition to glass (e.g. the claddingportion of a glass fiber). Suitable adhesion promoters includealkoxysilanes, mercapto-functional silanes, organotitanates, andzirconates. Representative adhesion promoters include mercaptoalkylsilanes or mercaptoalkoxy silanes such as3-mercaptopropyl-trialkoxysilane (e.g.,3-mercaptopropyl-trimethoxysilane, available from Gelest (Tullytown,Pa.)); bis(trialkoxysilyl-ethyl)benzene; acryloxypropyltrialkoxysilane(e.g., (3-acryloxypropyl)-trimethoxysilane, available from Gelest),methacryloxypropyltrialkoxysilane, vinyltrialkoxysilane,bis(trialkoxysilylethyl)hexane, allyltrialkoxysilane,styrylethyltrialkoxysilane, and bis(trimethoxysilylethyl)benzene(available from United Chemical Technologies (Bristol, Pa.)); see U.S.Pat. No. 6,316,516, the disclosure of which is hereby incorporated byreference in its entirety herein.

The adhesion promoter is present in the primary coating composition inan amount between 0.02 wt % and 10.0 wt %, or between 0.05 wt % and 4.0wt %, or between 0.1 wt % and 4.0 wt %, or between 0.1 wt % and 3.0 wt%, or between 0.1 wt % and 2.0 wt %, or between 0.1 wt % and 1.0 wt %,or between 0.5 wt % and 4.0 wt %, or between 0.5 wt % and 3.0 wt %, orbetween 0.5 wt % and 2.0 wt %, or between 0.5 wt % and 1.0 wt %.

A representative antioxidant is thiodiethylenebis[3-(3,5-di-tert-butyl)-4-hydroxy-phenyl) propionate] (e.g., IRGANOX1035, available from BASF). In some aspects, an antioxidant is presentin the coating composition in an amount greater than 0.25 wt %, orgreater than 0.50 wt %, or greater than 0.75 wt %, or greater than 1.0wt %, or an amount in the range from 0.25 wt % to 3.0 wt %, or an amountin the range from 0.50 wt % to 2.0 wt %, or an amount in the range from0.75 wt % to 1.5 wt %.

Primary Coating—Properties. Relevant properties of the primary coatinginclude radius, thickness, Young's modulus, and in situ modulus.

The radius r₅ of the primary coating is less than or equal to 75.0 μm,or less than or equal to 70.0 μm, or less than or equal to 65.0 μm, orless than or equal to 60.0 μm, or less than or equal to 55.0 μm, or lessthan or equal to 50.0 μm, or in the range from 45.0 μm to 75.0 μm, or inthe range from 45.0 μm to 65.0 μm, or in the range from 45.0 μm to 60.0μm, or in the range from 45.0 μm to 55.0 μm, or in the range from 50.0μm to 70.0 μm, or in the range from 50.0 μm to 65.0 μm.

To facilitate decreases in the diameter of the optical fiber, it ispreferable to minimize the thickness r₅−r₄ of the primary coating. Thethickness r₅−r₄ of the primary coating is greater than or equal to 8.0μm (e.g., greater than or equal to 8.5 μm, greater than or equal to 9.0μm, greater than or equal to 9.5 μm, greater than or equal to 10.0 μm,etc.), and less than or equal to 30.0 μm, or less than or equal to 25.0μm, or less than or equal to 20.0 μm, or less than or equal to 15.0 μm,or less than or equal to 10.0 μm, or in the range from 8.0 μm to 25.0μm, or in the range from 9.0 μm to 20.0 μm, or in the range from 10.0 μmto 17.0 μm.

In some embodiments, to facilitate effective buffering of stress andprotection of the glass fiber, it is preferable for the primary coatingto have a low Young's modulus and/or a low in situ modulus E_(P). TheYoung's modulus of the primary coating is less than or equal to 0.7 MPa,or less than or equal to 0.6 MPa, or less than or equal to 0.5 MPa, orless than or equal to 0.4 MPa, or in the range from 0.2 MPa to 0.7 MPa,or in the range from 0.3 MPa to 0.6 MPa. The in situ modulus E_(P) ofthe primary coating is less than or equal to 0.35 MPa, or less than orequal to 0.30 MPa, or less than or equal to 0.25 MPa, or less than orequal to 0.20 MPa, or less than or equal to 0.15 MPa, or less than orequal to 0.10 MPa, or in the range from 0.05 MPa to 0.25 MPa, or in therange from 0.10 MPa to 0.20 MPa.

In some other embodiments, the primary coating can act as a “spring”that couples the stiff glass portion (e.g., the second outer claddingregion 58) to the relatively stiff secondary coating that has an in situmodulus E_(P) greater than 1200 MPa, or greater than 1400 MPa, orgreater than 1500 MPa, or greater than 1800 MPa. The spring constant ofthe primary coating is defined as χ_(P)=E_(P)*d₄/t_(P), where d₄ is thediameter of the glass portion of the fiber (i.e., d₄=2r_(4b)), and t_(P)and E_(P) are the thickness and in situ modulus, respectively, of theprimary coating. In some embodiments, the spring constant of the primarycoating has a value χ_(P)≤1.6 MPa, or χ_(P)≤1.5 MPa, or χ_(P)≤1.4 MPa,or χ_(P)≤1.3 MPa, or χ_(P)≤1.2 MPa, or χ_(P)≤1.1 MPa, or χ_(P)≤1.0 MPa,or χ_(P)≤0.9 MPa, or χ_(P)≤0.8 MPa, or χ_(P)≤0.7 MPa, or χ_(P)≤0.6 MPa,or 0.5 MPa≤χ_(P)≤1.5 MPa, or 0.5 MPa≤χ_(P)≤1.2 MPa, or 0.6 MPa≤χ_(P)≤1.0MPa. Such design can reduce the microbending losses and improvemicrobending resistance, since a small spring constant provides lowerdegree of coupling between the glass portion of the fiber and thesecondary coating.

Secondary Coating—Compositions. The secondary coating is a cured productof a curable secondary coating composition that includes a monomer, aphotoinitiator, an optional oligomer, and an optional additive. Thepresent disclosure describes optional oligomers for theradiation-curable secondary coating compositions, radiation-curablesecondary coating compositions, cured products of the radiation-curablesecondary coating compositions, optical fibers coated with aradiation-curable secondary coating composition, and optical fiberscoated with the cured product of a radiation-curable secondary coatingcomposition.

The secondary coating is formed as the cured product of aradiation-curable secondary coating composition that includes a monomercomponent with one or more monomers. The monomers preferably includeethylenically unsaturated compounds. The one or more monomers may bepresent in an amount of 50 wt % or greater, or in an amount from about60 wt % to about 99 wt %, or in an amount from about 75 wt % to about 99wt %, or in an amount from about 80 wt % to about 99 wt % or in anamount from about 85 wt % to about 99 wt %. In one embodiment, thesecondary coating is the radiation-cured product of a secondary coatingcomposition that contains urethane acrylate monomers.

The monomers include functional groups that are polymerizable groupsand/or groups that facilitate or enable crosslinking. The monomers aremonofunctional monomers or multifunctional monomers. In combinations oftwo or more monomers, the constituent monomers are monofunctionalmonomers, multifunctional monomers, or a combination of monofunctionalmonomers and multifunctional monomers. In one embodiment, the monomercomponent of the curable secondary coating composition includesethylenically unsaturated monomers. Suitable functional groups forethylenically unsaturated monomers include, without limitation,(meth)acrylates, acrylamides, N-vinyl amides, styrenes, vinyl ethers,vinyl esters, acid esters, and combinations thereof.

In one embodiment, the monomer component of the curable secondarycoating composition includes ethylenically unsaturated monomers. Themonomers include functional groups that are polymerizable groups and/orgroups that facilitate or enable crosslinking. The monomers aremonofunctional monomers or multifunctional monomers. In combinations oftwo or more monomers, the constituent monomers are monofunctionalmonomers, multifunctional monomers, or a combination of monofunctionalmonomers and multifunctional monomers. Suitable functional groups forethylenically unsaturated monomers include, without limitation,(meth)acrylates, acrylamides, N-vinyl amides, styrenes, vinyl ethers,vinyl esters, acid esters, and combinations thereof.

Exemplary monofunctional ethylenically unsaturated monomers for thecurable secondary coating composition include, without limitation,hydroxyalkyl acrylates such as 2-hydroxyethyl-acrylate,2-hydroxypropyl-acrylate, and 2-hydroxybutyl-acrylate; long- andshort-chain alkyl acrylates such as methyl acrylate, ethyl acrylate,propyl acrylate, isopropyl acrylate, butyl acrylate, amyl acrylate,isobutyl acrylate, t-butyl acrylate, pentyl acrylate, isoamyl acrylate,hexyl acrylate, heptyl acrylate, octyl acrylate, isooctyl acrylate,2-ethylhexyl acrylate, nonyl acrylate, decyl acrylate, isodecylacrylate, undecyl acrylate, dodecyl acrylate, lauryl acrylate, octadecylacrylate, and stearyl acrylate; aminoalkyl acrylates such asdimethylaminoethyl acrylate, diethylaminoethyl acrylate, and7-amino-3,7-dimethyloctyl acrylate; alkoxyalkyl acrylates such asbutoxyethyl acrylate, phenoxyethyl acrylate (e.g., SR339, SartomerCompany, Inc.), and ethoxyethoxyethyl acrylate; single and multi-ringcyclic aromatic or non-aromatic acrylates such as cyclohexyl acrylate,benzyl acrylate, dicyclopentadiene acrylate, dicyclopentanyl acrylate,tricyclodecanyl acrylate, bomyl acrylate, isobornyl acrylate (e.g.,SR423, Sartomer Company, Inc.), tetrahydrofiurfuryl acrylate (e.g.,SR285, Sartomer Company, Inc.), caprolactone acrylate (e.g., SR495,Sartomer Company, Inc.), and acryloylmorpholine; alcohol-based acrylatessuch as polyethylene glycol monoacrylate, polypropylene glycolmonoacrylate, methoxyethylene glycol acrylate, methoxypolypropyleneglycol acrylate, methoxypolyethylene glycol acrylate, ethoxydiethyleneglycol acrylate, and various alkoxylated alkylphenol acrylates such asethoxylated(4) nonylphenol acrylate (e.g., Photomer 4066, IGM Resins);acrylamides such as diacetone acrylamide, isobutoxymethyl acrylamide,N,N′-dimethyl-aminopropyl acrylamide, N,N-dimethyl acrylamide, N,Ndiethyl acrylamide, and t-octyl acrylamide; vinylic compounds such asN-vinylpyrrolidone and N-vinylcaprolactam; and acid esters such asmaleic acid ester and fumaric acid ester. With respect to the long andshort chain alkyl acrylates listed above, a short chain alkyl acrylateis an alkyl group with 6 or less carbons and a long chain alkyl acrylateis an alkyl group with 7 or more carbons.

Representative radiation-curable ethylenically unsaturated monomersincluded alkoxylated monomers with one or more acrylate or methacrylategroups. An alkoxylated monomer is one that includes one or morealkoxylene groups, where an alkoxylene group has the form —O—R— and R isa linear or branched hydrocarbon. Examples of alkoxylene groups includeethoxylene (—O—CH₂—CH₂—), n-propoxylene (—O—CH₂—CH₂—CH₂—),isopropoxylene (—O—CH₂—CH(CH₃)—), etc. As used herein, the degree ofalkoxylation refers to the number of alkoxylene groups in the monomer.In one embodiment, the alkoxylene groups are bonded consecutively in themonomer.

Representative multifunctional ethylenically unsaturated monomers forthe curable secondary coating composition include, without limitation,alkoxylated bisphenol-A diacrylates, such as ethoxylated bisphenol-Adiacrylate, and alkoxylated trimethylolpropane triacrylates, such asethoxylated trimethylolpropane triacrylate, with the degree ofalkoxylation being 2 or greater, or 4 or greater, or 6 or greater, orless than 16 or less than 12, or less than 8, or less than 5, or in therange from 2 to 16, or in the range from 2 to 12, or in the range from 2to 8, or in the range from 2 to 4, or in the range from 3 to 12, or inthe range from 3 to 8, or in the range from 3 to 5, or in the range from4 to 12, or in the range from 4 to 10, or in the range from 4 to 8.

Multifunctional ethylenically unsaturated monomers for the curablesecondary coating composition include, without limitation, alkoxylatedbisphenol A diacrylates, such as ethoxylated bisphenol A diacrylate,with the degree of alkoxylation being 2 or greater. The monomercomponent of the secondary coating composition may include ethoxylatedbisphenol A diacrylate with a degree of ethoxylation ranging from 2 toabout 30 (e.g. SR349, SR601, and SR602 available from Sartomer Company,Inc. West Chester, Pa. and Photomer 4025 and Photomer 4028, availablefrom IGM Resins), or propoxylated bisphenol A diacrylate with the degreeof propoxylation being 2 or greater; for example, ranging from 2 toabout 30; methylolpropane polyacrylates with and without alkoxylationsuch as ethoxylated trimethylolpropane triacrylate with the degree ofethoxylation being 3 or greater; for example, ranging from 3 to about 30(e.g., Photomer 4149, IGM Resins, and SR499, Sartomer Company, Inc.);propoxylated-trimethylolpropane triacrylate with the degree ofpropoxylation being 3 or greater; for example, ranging from 3 to 30(e.g., Photomer 4072, IGM Resins and SR492, Sartomer);ditrimethylolpropane tetraacrylate (e.g., Photomer 4355, IGM Resins);alkoxylated glyceryl triacrylates such as propoxylated glyceryltriacrylate with the degree of propoxylation being 3 or greater (e.g.,Photomer 4096, IGM Resins and SR9020, Sartomer); erythritolpolyacrylates with and without alkoxylation, such as pentaerythritoltetraacrylate (e.g., SR295, available from Sartomer Company, Inc. (WestChester, Pa.)), ethoxylated pentaerythritol tetraacrylate (e.g., SR494,Sartomer Company, Inc.), and dipentaerythritol pentaacrylate (e.g.,Photomer 4399, IGM Resins, and SR399, Sartomer Company, Inc.);isocyanurate polyacrylates formed by reacting an appropriate functionalisocyanurate with an acrylic acid or acryloyl chloride, such astris-(2-hydroxyethyl) isocyanurate triacrylate (e.g., SR368, SartomerCompany, Inc.) and tris-(2-hydroxyethyl) isocyanurate diacrylate;alcohol polyacrylates with and without alkoxylation such astricyclodecane dimethanol diacrylate (e.g., CD406, Sartomer Company,Inc.) and ethoxylated polyethylene glycol diacrylate with the degree ofethoxylation being 2 or greater; for example, ranging from about 2 to30; epoxy acrylates formed by adding acrylate to bisphenol Adiglycidylether and the like (e.g., Photomer 3016, IGM Resins); andsingle and multi-ring cyclic aromatic or non-aromatic polyacrylates suchas dicyclopentadiene diacrylate and dicyclopentane diacrylate.

In some embodiments, the curable secondary coating composition includesa multifunctional monomer with three or more curable functional groupsin an amount greater than 2.0 wt %, or greater than 5.0 wt %, or greaterthan 7.5 wt %, or greater than 10 wt %, or greater than 15 wt %, orgreater than 20 wt %, or in the range from 2.0 wt % to 25 wt %, or inthe range from 5.0 wt % to 20 wt %, or in the range from 8.0 wt % to 15wt %. In a preferred embodiment, each of the three or more curablefunctional groups is an acrylate group.

In some embodiments, the curable secondary coating composition includesa trifunctional monomer in an amount greater than 2.0 wt %, or greaterthan 5.0 wt %, or greater than 7.5 wt %, or greater than 10 wt %, orgreater than 15 wt %, or greater than 20 wt %, or in the range from 2.0wt % to 25 wt %, or in the range from 5.0 wt % to 20 wt %, or in therange from 8.0 wt % to 15 wt %. In a preferred embodiment, thetrifunctional monomer is a triacrylate monomer.

In some embodiments, the curable secondary coating composition includesa difunctional monomer in an amount greater than 55 wt %, or greaterthan 60 wt %, or greater than 65 wt %, or greater than 70 wt %, or inthe range from 55 wt % to 80 wt %, or in the range from 60 wt % to 75 wt%, and further includes a trifunctional monomer in an amount in therange from 2.0 wt % to 25 wt %, or in the range from 5.0 wt % to 20 wt%, or in the range from 8.0 wt % to 15 wt %. In a preferred embodiment,the difunctional monomer is a diacrylate monomer and the trifunctionalmonomer is a triacrylate monomer. Preferred diacrylate monomers includealkoxylated bisphenol-A diacrylates. Preferred triacrylate monomersinclude alkoxylated trimethylolpropane triacrylates and isocyanuratetriacrylates. Preferably the curable secondary coating composition lacksan alkoxylated bisphenol-A diacrylate having a degree of alkoxylationgreater than 17, or greater than 20, or greater than 25, or in the rangefrom 15 to 40, or in the range from 20 to 35.

A preferred difunctional monomer is an alkoxylated bisphenol-Adiacrylate. Alkoxylated bisphenol-A diacrylate has the general formula(XIII):

where R₁ and R₂ are alkylene groups, R₁—O and R₂—O are alkoxylenegroups, and R₃ is H. Any two of the groups R₁, R₂, and R₃ are the sameor different. In one embodiment, the groups R₁ and R₂ are the same. Thenumber of carbons in each of the groups R₁ and R₂ is in the range from 1to 8, or in the range from 2 to 6, or in the range from 2 to 4. Thedegree of alkoxylation is ½(x+y). The values of x and y are the same ordifferent. In one embodiment, x and y are the same.

A preferred trifunctional monomer is an alkoxylated trimethylolpropanetriacrylate. Alkoxylated trimethylolpropane triacrylate has the generalformula (XIV):

where R₁ and R₂ are alkylene groups, O—R₁, O—R₂, and O—R₃ are alkoxylenegroups. Any two of the groups R₁, R₂, and R₃ are the same or different.In one embodiment, the groups R₁, R₂, and R₃ are the same. The number ofcarbons in the each of the groups R₁, R₂, and R₃ is in the range from 1to 8, or in the range from 2 to 6, or in the range from 2 to 4. Thedegree of alkoxylation is ⅓(x+y+z). The values of any two of x, y and zare the same or different. In one embodiment, x, y, and z are the same.

Another preferred trifunctional monomer is a tris[(acryloyloxy)alkyl]isocyanurate. Tris[(acryloyloxy)alkyl] isocyanurates are also referredto as tris[n-hydroxyalkyl) isocyanurate triacrylates. A representativetris[(acryloyloxy)alkyl] isocyanurate is tris[2-hydroxyethyl)isocyanurate triacrylate, which has the general formula (XV):

In formula (III), an ethylene linkage (—CH₂—CH₂—) bonds each acryloyloxygroup to a nitrogen of the isocyanurate ring. In other embodiments oftris[(acryloyloxy)alkyl] isocyanurates, alkylene linkages other thanethylene bond the acryloyloxy groups to nitrogen atoms of theisocyanurate ring. The alkylene linkages for any two of the threealkylene linkages are the same or different. In one embodiment, thethree alkylene linkages are the same. The number of carbons in each ofthe alkylene linkages is in the range from 1 to 8, or in the range from2 to 6, or in the range from 2 to 4.

In one embodiment, the curable secondary composition includes analkoxylated bisphenol-A diacrylate monomer in an amount greater than 55wt %, or greater than 60 wt %, or greater than 65 wt %, or greater than70 wt %, or in the range from 55 wt % to 80 wt %, or in the range from60 wt % to 75 wt %, and further includes an alkoxylatedtrimethylolpropane triacrylate monomer in an amount in the range from2.0 wt % to 25 wt %, or in the range from 5.0 wt % to 20 wt %, or in therange from 8.0 wt % to 15 wt %. Preferably the curable secondary coatingcomposition lacks an alkoxylated bisphenol-A diacrylate having a degreeof alkoxylation greater than 17, or greater than 20, or greater than 25,or in the range from 15 to 40, or in the range from 20 to 35.

In one embodiment, the curable secondary composition includes analkoxylated bisphenol-A diacrylate monomer in an amount greater than 55wt %, or greater than 60 wt %, or greater than 65 wt %, or greater than70 wt %, or in the range from 55 wt % to 80 wt %, or in the range from60 wt % to 75 wt %, and further includes a tris[(acryloyloxy)alkyl]isocyanurate monomer in an amount in the range from 2.0 wt % to 25 wt %,or in the range from 5.0 wt % to 20 wt %, or in the range from 8.0 wt %to 15 wt %. Preferably the curable secondary coating composition lacksan alkoxylated bisphenol-A diacrylate having a degree of alkoxylationgreater than 17, or greater than 20, or greater than 25, or in the rangefrom 15 to 40, or in the range from 20 to 35.

In one embodiment, the curable secondary composition includes analkoxylated bisphenol-A diacrylate monomer in an amount greater than 55wt %, or greater than 60 wt %, or greater than 65 wt %, or greater than70 wt %, or in the range from 55 wt % to 80 wt %, or in the range from60 wt % to 75 wt %, and further includes tris(2-hydroxyethyl)isocyanurate triacrylate monomer in an amount in the range from 2.0 wt %to 25 wt %, or in the range from 5.0 wt % to 20 wt %, or in the rangefrom 8.0 wt % to 15 wt %. Preferably the curable secondary coatingcomposition lacks an alkoxylated bisphenol-A diacrylate having a degreeof alkoxylation greater than 17, or greater than 20, or greater than 25,or in the range from 15 to 40, or in the range from 20 to 35.

In one embodiment, the curable secondary composition includesbisphenol-A epoxy diacrylate monomer in an amount greater than 5.0 wt %,or greater than 10 wt %, or greater than 15 wt %, or in the range from5.0 wt % to 20 wt % or in the range from 8 wt % to 17 wt %, or in therange from 10 wt % to 15 wt %, and further includes an alkoxylatedbisphenol-A diacrylate monomer in an amount greater than 55 wt %, orgreater than 60 wt %, or greater than 65 wt %, or greater than 70 wt %,or in the range from 55 wt % to 80 wt %, or in the range from 60 wt % to75 wt %, and further includes an alkoxylated trimethylolpropanetriacrylate monomer in an amount in the range from 2.0 wt % to 25 wt %,or in the range from 5.0 wt % to 20 wt %, or in the range from 8.0 wt %to 15 wt %. Preferably the curable secondary coating composition lacksan alkoxylated bisphenol-A diacrylate having a degree of alkoxylationgreater than 17, or greater than 20, or greater than 25, or in the rangefrom 15 to 40, or in the range from 20 to 35.

In one embodiment, the curable secondary composition includesbisphenol-A epoxy diacrylate monomer in an amount greater than 5.0 wt %,or greater than 10 wt %, or greater than 15 wt %, or in the range from5.0 wt % to 20 wt % or in the range from 8 wt % to 17 wt %, or in therange from 10 wt % to 15 wt %, and further includes an alkoxylatedbisphenol-A diacrylate monomer in an amount greater than 55 wt %, orgreater than 60 wt %, or greater than 65 wt %, or greater than 70 wt %,or in the range from 55 wt % to 80 wt %, or in the range from 60 wt % to75 wt %, and further includes a tris[(acryloyloxy)alkyl] isocyanuratemonomer in an amount in the range from 2.0 wt % to 25 wt %, or in therange from 5.0 wt % to 20 wt %, or in the range from 8.0 wt % to 15 wt%. Preferably the curable secondary coating composition lacks analkoxylated bisphenol-A diacrylate having a degree of alkoxylationgreater than 17, or greater than 20, or greater than 25, or in the rangefrom 15 to 40, or in the range from 20 to 35.

In one embodiment, the curable secondary composition includesbisphenol-A epoxy diacrylate monomer in an amount greater than 5.0 wt %,or greater than 10 wt %, or greater than 15 wt %, or in the range from5.0 wt % to 20 wt % or in the range from 8 wt % to 17 wt %, or in therange from 10 wt % to 15 wt %, and further includes an alkoxylatedbisphenol-A diacrylate monomer in an amount greater than 55 wt %, orgreater than 60 wt %, or greater than 65 wt %, or greater than 70 wt %,or in the range from 55 wt % to 80 wt %, or in the range from 60 wt % to75 wt %, and further includes tris(2-hydroxyethyl) isocyanuratetriacrylate monomer in an amount in the range from 2.0 wt % to 25 wt %,or in the range from 5.0 wt % to 20 wt %, or in the range from 8.0 wt %to 15 wt %. Preferably the curable secondary coating composition lacksan alkoxylated bisphenol-A diacrylate having a degree of alkoxylationgreater than 17, or greater than 20, or greater than 25, or in the rangefrom 15 to 40, or in the range from 20 to 35.

The curable secondary coating composition also includes a photoinitiatorand optionally includes additives such as anti-oxidant(s), opticalbrightener(s), amine synergist(s), tackifier(s), catalyst(s), a carrieror surfactant, and a stabilizer as described above in connection withthe curable primary coating composition.

Secondary Coating—Properties. Relevant properties of the secondarycoating include radius, thickness, Young's modulus, tensile strength,yield strength, elongation at yield, glass transition temperature, andpuncture resistance

The radius r₆ of the secondary coating is less than or equal to 100.0μm, or less than or equal to 95.0 μm, or less than or equal to 90.0 μm,or less than or equal to 85.0 μm, or less than or equal to 80.0 μm, orless than or equal to 75.0 μm, or less than or equal to 70.0 μm, or lessthan or equal to 65.0 μm, or less than or equal to 60.0 μm.

To facilitate decreases in the diameter of the optical fiber, it ispreferable to minimize the thickness (r₆−r₅) of the secondary coating.The thickness (r₆−r₅) of the secondary coating is greater than or equalto 7.0 μm (e.g., greater than or equal to 8.0 μm, greater than or equalto 9.0 μm, greater than or equal to 10.0 μm, etc.), and less than orequal to 30.0 μm, or less than or equal to 25.0 μm, or less than orequal to 20.0 μm, or less than or equal to 15.0 μm, or in the range from7.0 μm to 25.0 μm, or in the range from 8.0 μm to 20.0 μm, or in therange from 9.0 μm to 18.0 μm, or in the range from 10.0 μm to 16.0 μm.

A factor promoting puncture resistance and low microbend loss is theratio of the thickness (r₅−r₄) of the primary coating to the thickness(r₆−r₅) of the secondary coating. The ratio of the thickness (r₅−r₄) ofthe primary coating to the thickness (r₆−r₅) of the secondary coating isin a range from 0.3 to 1.7, or in a range from 0.5 to 1.5, or in a rangefrom 0.7 to 1.2.

To facilitate puncture resistance and high protective function, it ispreferable for the secondary coating to have a high Young's modulusand/or a high in situ modulus E_(S). The Young's modulus of thesecondary coating is greater than or equal to 1600 MPa, or greater thanor equal to 1800 MPa, or greater than or equal to 2000 MPa, or greaterthan or equal to 2200 MPa, or in the range from 1600 MPa to 2800 MPa, orin the range from 1800 MPa to 2600 MPa. In some embodiments, the in situmodulus E_(S) of the secondary coating is greater than or equal to 1200MPa, or greater than or equal to 1500 MPa, or greater than or equal to1800 MPa, or greater than or equal to 2000 MPa, or in the range from1200 MPa to 2800 MPa, or in the range from 1500 MPa to 2600 MPa.

Tertiary Coating—Properties. As described above, the optical fiber canoptionally have a tertiary coating situated on top of the secondarycoating. In some embodiments, the tertiary coating is an ink layer or acoating containing ink. A sum of the thicknesses of the secondarycoating and the tertiary coating can be larger than or equal to 10 μm,or larger than or equal to 12 μm, or in a range from 12 μm to 30 μm. Thecombined cross-sectional areas of the secondary coating and optionaltertiary coating can be larger than or equal to 20000 μm², or largerthan or equal to 25000 μm², or larger than or equal to 30000 μm², whichadvantageously ensures that the fiber has sufficient punctureresistance.

Design Examples—Glass Fiber

Five modeled design examples Ex. 1 through Ex. 5 of the single modeoptical fiber 100 with different core/cladding designs and opticalattributes are set forth in Table 1 below. Ex. 1 through Ex. 5 aregraded-index fibers having a relative refractive index profile of thetype shown in FIG. 7C. Ex. 1 through Ex. 5 each comprises an updopedgraded-index core, an undoped inner cladding, a downdopeddepressed-index cladding (corresponding to a trench), an undoped firstouter cladding, and an updoped second outer cladding (TiO₂-dopedsilica).

TABLE 1 Core/Cladding Design Examples of Glass Fibers Parameter Ex. 1Ex. 2 Ex. 3 Ex. 4 Ex. 5 Radius of core r₁ (nm) 4.33 4.38 4.26 4.37 4.29Core Alpha α 10.07 10.28 11.32 10.85 9.81 Core Index maximum Δ_(lmax)(%) 0.399 0.401 0.394 0.391 0.382 Core Volume V₁ (%-μm2) 6.23 6.43 6.086.29 5.82 Radius of inner cladding r₂ (μm) 9.04 9.38 10.47 10.19 10.64Index of inner cladding Δ₂ (%) 0.00 0.00 0.00 0.00 0.00 Radius ofdepressed-index 14.71 14.90 15.88 16.28 17.83 cladding r₃ (μm) Index ofdepressed-index −0.443 −0.394 −0.383 −0.417 −0.292 cladding Δ₃ (%)Trench Volume V₃ (%-μm²) −59.7 −52.8 −54.6 −67.1 −59.8 Radius of firstouter cladding r_(4a) (μm) 37 37 37 37 37 Index of first outer claddingΔ_(4a) (%) 0.00 0.00 0.00 0.00 0.00 Radius of second outer cladding 4040 40 40 40 r_(4b) (μm) Index of second outer cladding 1.92 1.92 1.921.92 1.92 Δ_(4b) (%) MFD at 1310 nm (μm) 8.45 8.50 8.52 8.59 8.61 MFD at1550 nm (μm) 9.43 9.49 9.61 9.65 9.76 Dispersion at 1310 nm 0.56 0.51−0.18 0.22 −0.47 (ps/nm/km) Dispersion Slope at 1310 nm 0.090 0.0900.088 0.089 0.088 (ps/nm²/km) Zero Dispersion Wavelength (nm) 1304 13041312 1307 1315 LP11 Therotical Cutoff 1245 1269 1248 1264 1224Wavelength (nm) λ_(CF) (nm) 1240 1260 1240 1260 1220 Bend Loss at 1550nm for 10 mm 0.049 0.072 0.082 0.030 0.078 diameter mandrel (dB/turn)

Measurement of Stresses in Optical Fiber

Residual stresses in optical fibers are induced due to the viscosity andcoefficient of thermal expansion differences from radial compositiondistribution. The mismatch in the properties result in thermal andmechanical stresses induced during the drawing process of manufacturingoptical fibers. Residual stresses in optical fibers are measured usingwell-documented methods in literature and familiar to those skilled inthe art. These methods include measuring stresses using a polariscope orusing traverse interferometry. Details of method for measuring residualstresses in optical fibers using polariscope are described in Park etal., Applied Optics, 41 (1), 21-26 (2002) and Chu and Whitbread, AppliedOptics, 21 (23), 4241 (1982). The method entails immersing the opticalfiber in an index matching fluid and impinging a light from a lightsource onto the optical fiber laterally. The ray entering the opticalfiber is split into two components due to stress-induced birefringence.The two components experience different refractive indices in theoptical fiber. As the light exits the fiber, the two components have aphase shift called retardation, with the magnitude of the retardationbeing a function of the ray incident position. The residual stresses canbe estimated from the measurements of retardation as a function of rayincident position. Alternate method of measuring residual stresses isusing the transverse interferometry method, as described in A. Yablon,“Advanced Fiber Characterization Technologies for Fiber Lasers andAmplifiers”, Conference on Advanced Solid State Lasers, Paper #ATh2A.45,Shanghai, China, 16-21 Nov. 2014. The measurement of stresses using thismethod can be performed using the IFA instrument available fromInterfiber Analysis LLC (Sharon, Mass., USA).

FIGS. 8A-8I illustrate axial stress of the single mode optical fiber 100along the radial position with various designs of the second outercladding, according to some embodiments of the present disclosure.

Referring to FIG. 8A, five lines indicating the axial stress vursesradial position of the five examples of the single mode optical fiberhas a core/cladding designs and optical attributes as Ex. 1-5 listedabove in Table 1. Specifically, the second outer cladding has athickness of 3 μm and a TiO₂ concentration 8 wt %. The five lines showthe axial stress distribution of the five exemplary single mode opticalfibers along the radial position under a 115 g draw tension.

Referring to FIG. 8B, three lines indicating the axial stress vursesradial position of the single mode optical fiber has a core/claddingdesigns and optical attributes as Ex. 1 listed above in Table 1.Specifically, while keeping the thickness of the second outer claddingas 3 microns and the draw tension as 115 g, the TiO₂ concentration ofthe second outer cladding is varied to show the changes of the axialstress of the single mode optical fiber. The dotted line shows the axialstress distribution of the single mode optical fiber with a 4 wt % TiO₂concentration of the second outer cladding, the dashed line shows theaxial stress distribution of the single mode optical fiber with an 8 wt% TiO₂ concentration of the second outer cladding, and the solid lineshows the axial stress distribution of the single mode optical fiberwith a 12 wt % TiO₂ concentration of the second outer cladding.

Referring to FIG. 8C, three lines indicating the axial stress vursesradial position of the single mode optical fiber has a core/claddingdesigns and optical attributes as Ex. 1 listed above in Table 1.Specifically, while keeping the TiO₂ concentration as 8 wt % and thedraw tension as 115 g, the thickness of the second outer cladding dopedwith TiO₂ is varied to show the changes of the axial stress of thesingle mode optical fiber. The dotted line shows the axial stressdistribution of the single mode optical fiber with a 3-μm-thick secondouter cladding, the dashed line shows the axial stress distribution ofthe single mode optical fiber with a 5-μm-thick second outer cladding,and the solid line shows the axial stress distribution of the singlemode optical fiber with a 7-μm-thick second outer cladding.

Referring to FIG. 8D, five lines indicating the axial stress vursesradial position of the five examples of the single mode optical fiberhas a core/cladding designs and optical attributes as Ex. 1-5 listedabove in Table 1. Specifically, the second outer cladding has athickness of 3 μm and a TiO₂ concentration 8 wt %. The five lines showthe axial stress distribution of the five exemplary single mode opticalfibers along the radial position under a 75 g draw tension.

Referring to FIG. 8E, three lines indicating the axial stress vursesradial position of the single mode optical fiber has a core/claddingdesigns and optical attributes as Ex. 1 listed above in Table 1.Specifically, while keeping the thickness of the second outer claddingas 3 microns and the draw tension as 75 g, the TiO₂ concentration of thesecond outer cladding is varied to show the changes of the axial stressof the single mode optical fiber. The dotted line shows the axial stressdistribution of the single mode optical fiber with a 4 wt % TiO₂concentration of the second outer cladding, the dashed line shows theaxial stress distribution of the single mode optical fiber with an 8 wt% TiO₂ concentration of the second outer cladding, and the solid lineshows the axial stress distribution of the single mode optical fiberwith a 12 wt % TiO₂ concentration of the second outer cladding.

Referring to FIG. 8F, three lines indicating the axial stress vursesradial position of the single mode optical fiber has a core/claddingdesigns and optical attributes as Ex. 1 listed above in Table 1.Specifically, while keeping the TiO₂ concentration as 8 wt % and thedraw tension as 75 g, the thickness of the second outer cladding dopedwith TiO₂ is varied to show the changes of the axial stress of thesingle mode optical fiber. The dotted line shows the axial stressdistribution of the single mode optical fiber with a 3-μm-thick secondouter cladding, the dashed line shows the axial stress distribution ofthe single mode optical fiber with a 5-μm-thick second outer cladding,and the solid line shows the axial stress distribution of the singlemode optical fiber with a 7-μm-thick second outer cladding.

Referring to FIG. 8G, five lines indicating the axial stress vursesradial position of the five examples of the single mode optical fiberhas a core/cladding designs and optical attributes as Ex. 1-5 listedabove in Table 1. Specifically, the second outer cladding has athickness of 3 μm and a TiO₂ concentration 8 wt %. The five lines showthe axial stress distribution of the five exemplary single mode opticalfibers along the radial position under a 25 g draw tension.

Referring to FIG. 8H, three lines indicating the axial stress vursesradial position of the single mode optical fiber has a core/claddingdesigns and optical attributes as Ex. 1 listed above in Table 1.Specifically, while keeping the thickness of the second outer claddingas 3 microns and the draw tension as 25 g, the TiO₂ concentration of thesecond outer cladding is varied to show the changes of the axial stressof the single mode optical fiber. The dotted line shows the axial stressdistribution of the single mode optical fiber with a 4 wt % TiO₂concentration of the second outer cladding, the dashed line shows theaxial stress distribution of the single mode optical fiber with an 8 wt% TiO₂ concentration of the second outer cladding, and the solid lineshows the axial stress distribution of the single mode optical fiberwith a 12 wt % TiO₂ concentration of the second outer cladding.

Referring to FIG. 8I, three lines indicating the axial stress vursesradial position of the single mode optical fiber has a core/claddingdesigns and optical attributes as Ex. 1 listed above in Table 1.Specifically, while keeping the TiO₂ concentration as 8 wt % and thedraw tension as 25 g, the thickness of the second outer cladding dopedwith TiO₂ is varied to show the changes of the axial stress of thesingle mode optical fiber. The dotted line shows the axial stressdistribution of the single mode optical fiber with a 3-μm-thick secondouter cladding, the dashed line shows the axial stress distribution ofthe single mode optical fiber with a 5-μm-thick second outer cladding,and the solid line shows the axial stress distribution of the singlemode optical fiber with a 7-μm-thick second outer cladding.

The following examples illustrate preparation of a representativeprimary and secondary coatings. Measurements of selected properties ofthe representative primary and secondary coatings are also described. Inaddition, modeled properties of glass fibers coated with primary andsecondary coatings at different coating thickness and modulus arepresented.

Design Examples—Primary Coating

Primary Coating—Oligomer. The primary coating composition included anoligomer.

For purposes of illustration, preparation of exemplary oligomers fromH12MDI (4,4′-methylene bis(cyclohexyl isocyanate), PPG4000(polypropylene glycol with M_(n)˜4000 g/mol) and HEA (2-hydroxyethylacrylate) in accordance with the reaction scheme hereinabove isdescribed. All reagents were used as supplied by the manufacturer andwere not subjected to further purification. H12MDI was obtained fromALDRICH. PPG4000 was obtained from COVESTRO and was certified to have anunsaturation of 0.004 meq/g as determined by the method described in thestandard ASTM D4671-16. HEA was obtained from KOWA.

The relative amounts of the reactants and reaction conditions werevaried to obtain a series of six oligomers. Oligomers with differentinitial molar ratios of the constituents were prepared with molar ratiosof the reactants satisfying H12MDI:HEA:PPG4000=n:m:p, where n was in therange from 3.0 to 4.0, m was in the range from 1.5n to 3 to 2.5n to 5,and p=2. In the reactions used to form the oligomers materials,dibutyltin dilaurate was used as a catalyst (at a level of 160 ppm basedon the mass of the initial reaction mixture) and2,6-di-tert-butyl-4-methylphenol (BHT) was used as an inhibitor (at alevel of 400 ppm based on the mass of the initial reaction mixture).

The amounts of the reactants used to prepare each of the six oligomersare summarized in Table 2 below. The six oligomers are identified byseparate Sample numbers 1-6. Corresponding sample numbers will be usedherein to refer to coating compositions and cured films formed fromcoating compositions that individually contain each of the sixoligomers. The corresponding mole numbers used in the preparation ofeach of the six samples are listed in Table 3 below. The mole numbersare normalized to set the mole number p of PPG4000 to 2.0.

TABLE 2 Reactants and Amounts for Exemplary Oligomer Samples 1-6 H12MDIHEA PPG4000 Sample (g) (g) (g) 1 22 6.5 221.5 2 26.1 10.6 213.3 3 26.110.6 213.3 4 27.8 12.3 209.9 5 27.8 12.3 209.9 6 22 6.5 221.5

TABLE 3 Mole Numbers for Oligomer Samples 1-6 H12MDI HEA PPG4000 MoleNumber Mole Number Mole Number Di-adduct Sample (n) (m) (p) (wt %) 1 3.02.0 2.0 1.3 2 3.7 3.4 2.0 3.7 3 3.7 3.4 2.0 3.7 4 4.0 4.0 2.0 5.0 5 4.04.0 2.0 5.0 6 3.0 2.0 2.0 1.3

The oligomers were prepared by mixing 4,4′-methylene bis(cyclohexylisocyanate), dibutyltin dilaurate and 2,6-di-tert-butyl-4 methylphenolat room temperature in a 500 mL flask. The 500 mL flask was equippedwith a thermometer, a CaCl₂ drying tube, and a stirrer. Whilecontinuously stirring the contents of the flask, PPG4000 was added overa time period of 30-40 minutes using an addition funnel. The internaltemperature of the reaction mixture was monitored as the PPG4000 wasadded and the introduction of PPG4000 was controlled to prevent excessheating (arising from the exothermic nature of the reaction). After thePPG4000 was added, the reaction mixture was heated in an oil bath atabout 70° C. to 75° C. for about 1 to 1½ hours. At various intervals,samples of the reaction mixture were retrieved for analysis by infraredspectroscopy (FTIR) to monitor the progress of the reaction bydetermining the concentration of unreacted isocyanate groups. Theconcentration of unreacted isocyanate groups was assessed based on theintensity of a characteristic isocyanate stretching mode near 2265 cm⁻¹.The flask was removed from the oil bath and its contents were allowed tocool to below 65° C. Addition of supplemental HEA was conducted toinsure complete quenching of isocyanate groups. The supplemental HEA wasadded dropwise over 2-5 minutes using an addition funnel. After additionof the supplemental HEA, the flask was returned to the oil bath and itscontents were again heated to about 70° C. to 75° C. for about 1 to 1½hours. FTIR analysis was conducted on the reaction mixture to assess thepresence of isocyanate groups and the process was repeated until enoughsupplemental HEA was added to fully react any unreacted isocyanategroups. The reaction was deemed complete when no appreciable isocyanatestretching intensity was detected in the FTIR measurement. The HEAamounts listed in Table 2 and Table 3 include the initial amount of HEAin the composition and any amount of supplemental HEA needed to quenchunreacted isocyanate groups.

The concentration (wt %) of di-adduct compound in each oligomer wasdetermined by gel permeation chromatography (GPC). A Waters Alliance2690 GPC instrument was used to determine the di-adduct concentration.The mobile phase was THF. The instrument included a series of threePolymer Labs columns. Each column had a length of 300 mm and an insidediameter of 7.5 mm. Two of the columns (columns 1 and 2) were sold underPart No. PL1110-6504 by Agilent Technologies and were packed with PLgelMixed D stationary phase (polystyrene divinyl benzene copolymer, averageparticle size=5 μm, specified molecular weight range=200 g/mol to400,000 g/mol). The third column (column 3) was sold under Part No.PL1110-6520 by Agilent Technologies and was packed with PLgel 100Astationary phase (polystyrene divinyl benzene copolymer, averageparticle size=5 μm, specified molecular weight range=up to 4,000 g/mol).The columns were calibrated with polystyrene standards ranging from 162g/mol to 6,980,000 g/mol using EasiCal PS-1 & 2 polymer calibrant kits(Agilent Technologies Part Nos. PL2010-505 and PL2010-0601). The GPCinstrument was operated under the following conditions: flow rate=1.0mL/min, column temperature=40° C., injection volume=100 μL, and runtime=35 min (isocratic conditions). The detector was a Waters Alliance2410 differential refractometer operated at 40° C. and sensitivity level4. The samples were injected twice along with a THF+0.05% toluene blank.

The amount (wt %) of di-adduct in the oligomers was quantified using thepreceding GPC system and technique. A calibration curve was obtainedusing standard solutions containing known amounts of the di-adductcompound (HEA-H12MDI˜HEA) in THF. Standard solutions with di-adductconcentrations of 115.2 μg/g, 462.6 μg/g, 825.1 μg/g, and 4180 μg/g wereprepared. (As used herein, the dimension “μg/g” refers to μg ofdi-adduct per gram of total solution (di-adduct+THF)). Two 100 μLaliquots of each di-adduct standard solution were injected into thecolumn to obtain the calibration curve. The retention time of thedi-adduct was approximately 23 min and the area of the GPC peak of thedi-adduct was measured and correlated with di-adduct concentration. Alinear correlation of peak area as a function of di-adduct concentrationwas obtained (correlation coefficient (R²)=0.999564).

The di-adduct concentration in the oligomers was determined using thecalibration. Samples were prepared by diluting˜0.10 g of oligomericmaterial in THF to obtain a ˜1.5 g test solution. The test solution wasrun through the GPC instrument and the area of the peak associated withthe di-adduct compound was determined. The di-adduct concentration inunits of μg/g was obtained from the peak area and the calibration curve,and was converted to wt % by multiplying by the weight (g) of the testsolution and dividing by the weight of the sample of oligomeric materialbefore dilution with THF. The wt % of di-adduct compound present in eachof the six oligomers prepared in this example are reported in Table 2.

Through variation in the relative mole ratios of H12MDI, HEA, andPPG4000, the illustrative oligomers include a polyether urethanecompound of the type shown in molecular formula (IV) hereinabove and anenhanced concentration of di-adduct compound of the type shown inmolecular formula (V) hereinabove.

Primary Coating—Compositions. Oligomers corresponding to Samples 1-6were separately combined with other components to form a series of sixcoating compositions. The amount of each component in the coatingcomposition is listed in Table 4 below. The entry in Table 4 for theoligomer includes the combined amount of polyether urethane acrylatecompound and di-adduct compound present in the oligomer. A separatecoating composition was made for each of the six exemplary oligomerscorresponding to Samples 1-6, where the amount of di-adduct compound inthe oligomeric material corresponded to the amount listed in Table 3.

TABLE 4 Coating Composition Component Amount Oligomeric Material 49.10wt % Sartomer SR504 45.66 wt % V-CAP/RC  1.96 wt % TPO  1.47 wt %Irganox 1035  0.98 wt % adhesion promoter  0.79 wt % Tetrathiol  0.03 wt%

Sartomer SR504 is ethoxylated(4)nonylphenol acrylate (available fromSartomer). V-CAP/RC is N-vinylcaprolactam (available from ISPTechnologies). TPO is 2,4,6-trimethylbenzoyl)diphenyl phosphine oxide(available from BASF under the trade name Lucirin and functions as aphotoinitiator). Irganox 1035 is thiodiethylenebis[3-(3,5-di-tert-butyl)-4-hydroxy-phenyl) propionate] (available fromBASF) and functions as an antioxidant. The adhesion promoters were3-acryloxypropyl trimethoxysilane (available from Gelest) and3-mercaptopropyl trimethoxysilane (available from Aldrich).3-acryloxypropyl trimethoxysilane was used for Samples 1, 3, and 5.3-mercaptopropyl trimethoxysilane was used for Samples 2, 4, and 6.Tetrathiol is a catalyst quencher.

The coating compositions of Table 4 were each formulated using ahigh-speed mixer in an appropriate container heated to 60° C., with aheating band or heating mantle. In each case, the components wereweighed into the container using a balance and allowed to mix until thesolid components were thoroughly dissolved and the mixture appearedhomogeneous. The oligomer and monomers (SR504, NVC) of each compositionwere blended together for at least 10 minutes at 55° C. to 60° C. Thephotoinitiator, antioxidant, and catalyst quencher were then added, andblending was continued for one hour while maintaining a temperature of55° C. to 60° C. Finally, the adhesion promoter was added, and blendingwas continued for 30 minutes at 55° C. to 60° C. to form the coatingcompositions.

Primary Coating—Properties—Tensile Properties. Tensile properties(Young's modulus, tensile strength at yield, and elongation at yield)were measured on films formed by curing the six coating compositions.Separate films were formed from each coating composition. Wet films ofthe coating composition were cast on silicone release paper with the aidof a draw-down box having a gap thickness of about 0.005″. The wet filmswere cured with a UV dose of 1.2 J/cm² (measured over a wavelength rangeof 225 to 424 nm by a Light Bug model IL490 from International Light) bya Fusion Systems UV curing apparatus with a 600 W/in D-bulb (50% Powerand approximately 12 ft/min belt speed) to yield cured coatings in filmform. Cured film thickness was between about 0.0030″ and 0.0035″.

The films were aged (23° C., 50% relative humidity) for at least 16hours prior to testing. Film samples were cut to dimensions of 12.5cm×13 mm using a cutting template and a scalpel. Young's modulus,tensile strength at yield, and elongation at yield were measured at roomtemperature (approximately 20° C.) on the film samples using a MTSSintech tensile test instrument following procedures set forth in ASTMStandard D882-97. Young's modulus is defined as the steepest slope ofthe beginning of the stress-strain curve. Films were tested at anelongation rate of 2.5 cm/min with the initial gauge length of 5.1 cm.The results are shown in Table 5.

TABLE 5 Young's Modulus, Tensile Strength, and Elongation of FilmSamples Young's Modulus Tensile Strength Elongation Sample (MPa) (MPa)(%) 1 0.72 0.51 137.9 2 0.57 0.44 173 3 1.0 0.86 132.8 4 0.71 0.45 122.35 0.72 0.56 157.4 6 0.33 0.33 311.9

Primary Coating—Properties—In Situ Modulus. In situ modulus measurementsof primary coating composition Samples 2, 3, and 5 were completed. Insitu modulus measurements require forming the primary coatings on aglass fiber having a diameter of 125 μm. Each of Samples 2, 3, and 5 wasseparately applied as a primary coating composition to a glass fiber asthe glass fiber was being drawn. The fiber draw speed was 50 m/s. Theprimary coating compositions were cured using a stack of five LEDsources. Each LED source was operated at 395 nm and had an intensity of12 W/cm². Subsequent to application and curing of the primary coatingcompositions, a secondary coating composition was applied to each of thecured primary coatings and cured using UV sources to form a secondarycoating layer. The thickness of the primary coating was 32.5 μm and thethickness of the secondary coating was 26.0 μm.

The in situ modulus was measured using the following procedure. Asix-inch sample of fiber was obtained and a one-inch section from thecenter of the fiber was window stripped and wiped with isopropylalcohol. The window-stripped fiber was mounted on a sampleholder/alignment stage equipped with 10 mm×5 mm rectangular aluminumtabs that were used to affix the fiber. Two tabs were orientedhorizontally and positioned so that the short 5 mm sides were facingeach other and separated by a 5 mm gap. The window-stripped fiber waslaid horizontally on the sample holder across the tabs and over the gapseparating the tabs. The coated end of one side of the window-strippedregion of the fiber was positioned on one tab and extended halfway intothe 5 mm gap between the tabs. The one-inch window-stripped regionextended over the remaining half of the gap and across the opposing tab.After alignment, the sample was moved and a small dot of glue wasapplied to the half of each tab closest to the 5 mm gap. The fiber wasthen returned to position and the alignment stage was raised until theglue just touched the fiber. The coated end was then pulled away fromthe gap and through the glue such that the majority of the 5 mm gapbetween the tabs was occupied by the window-stripped region of thefiber. The portion of the window-stripped region remaining on theopposing tab was in contact with the glue. The very tip of the coatedend was left to extend beyond the tab and into the gap between the tabs.This portion of the coated end was not embedded in the glue and was theobject of the in situ modulus measurement. The glue was allowed to drywith the fiber sample in this configuration to affix the fiber to thetabs. After drying, the length of fiber fixed to each of the tabs wastrimmed to 5 mm. The coated length embedded in glue, the non-embeddedcoated length (the portion extending into the gap between the tabs), andthe primary diameter were measured.

The in situ modulus measurements were performed on a Rheometrics DMTA IVdynamic mechanical testing apparatus at a constant strain of 9e-6 l/sfor a time of forty-five minutes at room temperature (21° C.). The gaugelength was 15 mm. Force and the change in length were recorded and usedto calculate the in situ modulus of the primary coating. The tab-mountedfiber samples were prepared by removing any epoxy from the tabs thatwould interfere with the 15 mm clamping length of the testing apparatusto ensure that there was no contact of the clamps with the fiber andthat the sample was secured squarely to the clamps. The instrument forcewas zeroed out. The tab to which the non-coated end of the fiber wasaffixed was then mounted to the lower clamp (measurement probe) of thetesting apparatus and the tab to which the coated end of the fiber wasaffixed was mounted to the upper (fixed) clamp of the testing apparatus.The test was then executed and the sample was removed once the analysiswas completed.

The in situ modulus of primary coating Samples 2, 3, and 5 are listed inTable 6.

TABLE 6 In Situ Modulus of Selected Primary Coatings Sample In-SituModulus (MPa) 2 0.27 3 0.33 5 0.3

Design Examples—Secondary Coating

Secondary Coating Compositions. Representative curable secondary coatingcompositions are listed in Table 7.

TABLE 7 Secondary Coating Compositions Composition Component KA KB KC KDSR601 (wt %) 72.0 30.0 30.0 30.0 SR602 (wt %) 37.0 37.0 37.0 SR349 (wt%) 30.0 15.0 SR399 (wt %) 15.0 SR499 (wt %) 30.0 CD9038 (wt %) 10.0Photomer 3016 (wt %) 15.0 TPO (wt %) 1.5 Irgacure 184 (wt %) 1.5Irgacure 1850 (wt %) 3.0 3.0 3.0 Irganox 1035 (pph) 0.5 DC-190 (pph) 1.0SR601 is ethoxylated (4) bisphenol A diacrylate (a monomer). SR602 isethoxylated (10) bisphenol A diacrylate (a monomer). SR349 isethoxylated (2) bisphenol A diacrylate (a monomer). SR399 isdipentaerythritol pentaacrylate. SR499 is ethoxylated (6)trimethylolpropane triacrylate. CD9038 is ethoxylated (30) bisphenol Adiacrylate (a monomer). Photomer 3016 is bisphenol A epoxy diacrylate (amonomer). TPO is a photoinitiator. Irgacure 184 is1-hydroxycyclohexylphenyl ketone (a photoinitiator). Irgacure 1850 isbis(2,6-dimethoxybenzoyl)-2,4,4-trimethylpentylphosphine oxide (aphotoinitiator). Irganox 1035 is thiodiethylenebis(3,5-di-tert-butyl)-4-hydroxyhydrocinnamate (an antioxidant). DC190is silicone-ethylene oxide/propylene oxide copolymer (a slip agent). Theconcentration unit “pph” refers to an amount relative to a basecomposition that includes all monomers, oligomers, and photoinitiators.For example, for secondary coating composition KA, a concentration of1.0 pph for DC-190 corresponds to 1 g DC-190 per 100 g combined ofSR601, CD9038, Photomer 3016, TPO, and Irgacure 184.

A comparative curable secondary coating composition (A) and threerepresentative curable secondary coating compositions (SB, SC, and SD)within the scope of the disclosure are listed in Table 8.

TABLE 8 Secondary Coating Compositions Composition Component A SB SC SDPE210 (wt %) 15.0 15.0 15.0 15.0 M240 (wt %) 72.0 72.0 72.0 62.0 M2300(wt %) 10.0 — — — M3130 (wt %) — 10.0 — — M370 (wt %) — — 10.0 10.0 TPO(wt %) 1.5 1.5 1.5 1.5 Irgacure 184 (wt %) 1.5 1.5 1.5 1.5 Irganox 1035(pph) 0.5 0.5 0.5 0.5 DC-190 (pph) 1.0 1.0 1.0 1.0PE210 is bisphenol-A epoxy diacrylate (available from Miwon SpecialtyChemical, Korea), M240 is ethoxylated (4) bisphenol-A diacrylate(available from Miwon Specialty Chemical, Korea), M2300 is ethoxylated(30) bisphenol-A diacrylate (available from Miwon Specialty Chemical,Korea), M3130 is ethoxylated (3) trimethylolpropane triacrylate(available from Miwon Specialty Chemical, Korea), TPO (a photoinitiator)is (2,4,6-trimethylbenzoyl)diphenyl phosphine oxide (available fromBASF), Irgacure 184 (a photoinitiator) is 1-hydroxycyclohexyl-phenylketone (available from BASF), Irganox 1035 (an antioxidant) isbenzenepropanoic acid,3,5-bis(1,1-dimethylethyl)-4-hydroxythiodi-2,1-ethanediyl ester(available from BASF). DC190 (a slip agent) is silicone-ethyleneoxide/propylene oxide copolymer (available from Dow Chemical). Theconcentration unit “pph” refers to an amount relative to a basecomposition that includes all monomers and photoinitiators. For example,for secondary coating composition A, a concentration of 1.0 pph forDC-190 corresponds to 1 g DC-190 per 100 g combined of PE210, M240,M2300, TPO, and Irgacure 184.

Secondary Coating—Properties. The Young's modulus, tensile strength atbreak, and elongation at break of secondary coatings made from secondarycompositions A, KA, KB, KC, KD, SB, SC and SD were measured.

Secondary Coating—Properties—Measurement Techniques. Properties ofsecondary coatings were determined using the measurement techniquesdescribed below:

Tensile Properties. The curable secondary coating compositions werecured and configured in the form of cured rod samples for measurement ofYoung's modulus, tensile strength at yield, yield strength, andelongation at yield. The cured rods were prepared by injecting thecurable secondary composition into Teflon® tubing having an innerdiameter of about 0.025″. The rod samples were cured using a Fusion Dbulb at a dose of about 2.4 J/cm² (measured over a wavelength range of225-424 nm by a Light Bug model IL390 from International Light). Aftercuring, the Teflon® tubing was stripped away to provide a cured rodsample of the secondary coating composition. The cured rods were allowedto condition for 18-24 hours at 23° C. and 50% relative humidity beforetesting. Young's modulus, tensile strength at break, yield strength, andelongation at yield were measured using a Sintech MTS Tensile Tester ondefect-free rod samples with a gauge length of 51 mm, and a test speedof 250 mm/min. Tensile properties were measured according to ASTMStandard D882-97. The properties were determined as an average of atleast five samples, with defective samples being excluded from theaverage.

In Situ Modulus of Secondary Coating. For secondary coatings, the insitu modulus was measured using fiber tube-off samples prepared from thefiber samples. A 0.0055 inch Miller stripper was clamped downapproximately 1 inch from the end of the fiber sample. This one-inchregion of fiber sample was immersed into a stream of liquid nitrogen andheld for 3 seconds. The fiber sample was then removed and quicklystripped. The stripped end of the fiber sample was then inspected. Ifcoating remained on the glass portion of the fiber sample, the tube-offsample was deemed defective and a new tube-off sample was prepared. Aproper tube-off sample is one that stripped clean from the glass andconsisted of a hollow tube with primary and secondary coating. Theglass, primary and secondary coating diameter were measured from theend-face of the un-stripped fiber sample.

The fiber tube-off samples were run using a Rheometrics DMTA IVinstrument at a sample gauge length 11 mm to obtain the in situ modulusof the secondary coating. The width, thickness, and length weredetermined and provided as input to the operating software of theinstrument. The sample was mounted and run using a time sweep program atambient temperature (21° C.) using the following parameters:

-   -   Frequency: 1 Rad/sec    -   Strain: 0.3%    -   Total Time=120 sec.    -   Time Per Measurement=1 sec    -   Initial Static Force=15.0 g    -   Static>Dynamic Force by =10.0%        Once completed, the last five E′ (storage modulus) data points        were averaged. Each sample was run three times (fresh sample for        each run) for a total of fifteen data points. The averaged value        of the three runs was reported.

Puncture Resistance of Secondary Coating. Puncture resistancemeasurements were made on samples that included a glass fiber, a primarycoating, and a secondary coating. The glass fiber had a diameter of 125μm. The primary coating was formed from the reference primary coatingcomposition listed in Table 9 below. Samples with various secondarycoatings were prepared as described below. The thicknesses of theprimary coating and secondary coating were adjusted to vary thecross-sectional area of the secondary coating as described below. Theratio of the thickness of the secondary coating to the thickness of theprimary coating was maintained at about 0.8 for all samples.

The puncture resistance was measured using the technique described inthe article entitled “Quantifying the Puncture Resistance of OpticalFiber Coatings”, by G. Scott Glaesemann and Donald A. Clark, publishedin the Proceedings of the 52^(nd) International Wire & Cable Symposium,pp. 237-245 (2003). A summary of the method is provided here. The methodis an indentation method. A 4-centimeter length of optical fiber wasplaced on a 3 mm-thick glass slide. One end of the optical fiber wasattached to a device that permitted rotation of the optical fiber in acontrolled fashion. The optical fiber was examined in transmission under100× magnification and rotated until the secondary coating thickness wasequivalent on both sides of the glass fiber in a direction parallel tothe glass slide. In this position, the thickness of the secondarycoating was equal on both sides of the optical fiber in a directionparallel to the glass slide. The thickness of the secondary coating inthe directions normal to the glass slide and above or below the glassfiber differed from the thickness of the secondary coating in thedirection parallel to the glass slide. One of the thicknesses in thedirection normal to the glass slide was greater and the other of thethicknesses in the direction normal to the glass slide was less than thethickness in the direction parallel to the glass slide. This position ofthe optical fiber was fixed by taping the optical fiber to the glassslide at both ends and is the position of the optical fiber used for theindentation test.

Indentation was carried out using a universal testing machine (Instronmodel 5500R or equivalent). An inverted microscope was placed beneaththe crosshead of the testing machine. The objective of the microscopewas positioned directly beneath a 75° diamond wedge indenter that wasinstalled in the testing machine. The glass slide with taped fiber wasplaced on the microscope stage and positioned directly beneath theindenter such that the width of the indenter wedge was orthogonal to thedirection of the optical fiber. With the optical fiber in place, thediamond wedge was lowered until it contacted the surface of thesecondary coating. The diamond wedge was then driven into the secondarycoating at a rate of 0.1 mm/min and the load on the secondary coatingwas measured. The load on the secondary coating increased as the diamondwedge was driven deeper into the secondary coating until punctureoccurred, at which point a precipitous decrease in load was observed.The indentation load at which puncture was observed was recorded and isreported herein as grams of force. The experiment was repeated with theoptical fiber in the same orientation to obtain ten measurement points,which were averaged to determine a puncture resistance for theorientation. A second set of ten measurement points was taken byrotating the orientation of the optical fiber by 180°.

Microbending. In the wire mesh covered drum test, the attenuation oflight at wavelength of 1550 nm through a coated fiber having a length of750 m was determined at room temperature. The microbend inducedattenuation was determined by the difference between a zero-tensiondeployment and a high-tension deployment on the wire mesh drum. Separatemeasurements were made for two winding configurations. In the firstconfiguration, the fiber was wound in a zero-tension configuration on analuminum drum having a smooth surface and a diameter of approximately400 mm. The zero-tension winding configuration provided a stress-freereference attenuation for light passing through the fiber. Aftersufficient dwell time, an initial attenuation measurement was performed.In the second winding configuration, the fiber sample was wound to analuminum drum that was wrapped with fine wire mesh. For this deployment,the barrel surface of the aluminum drum was covered with wire mesh andthe fiber was wrapped around the wire mesh. The mesh was wrapped tightlyaround the barrel without stretching and was kept intact without holes,dips, tearing, or damage. The wire mesh material used in themeasurements was made from corrosion-resistant type 304 stainless steelwoven wire cloth and had the following characteristics: mesh per linearinch: 165×165, wire diameter: 0.0019″, width opening: 0.0041″, and openarea %: 44.0. A 750 m length of coated fiber was wound at 1 m/s on thewire mesh covered drum at 0.050 cm take-up pitch while applying 80(+/−1) grams of tension. The ends of the fiber were taped to maintaintension and there were no fiber crossovers. The points of contact of thewound fiber with the mesh impart stress to the fiber and the attenuationof light through the wound fiber is a measure of stress-induced(microbending) losses of the fiber. The wire drum measurement wasperformed after a dwell time of 1-hour. The increase in fiberattenuation (in dB/km) in the measurement performed in the secondconfiguration (wire mesh covered drum) relative to the firstconfiguration (smooth drum) was determined for each wavelength. Theaverage of three trials was determined at each wavelength and isreported as the wire mesh microbend loss.

Reference Primary Coating. In measurements of in situ glass transitiontemperature (T_(g)), puncture resistance, and wire mesh covered drummicrobending attenuation, the measurement samples included a primarycoating between the glass fiber and a secondary coating. The primarycoating composition had the formulation given in Table 9 and is typicalof commercially available primary coating compositions.

TABLE 9 Reference Primary Coating Composition Component AmountOligomeric Material 50.0 wt % SR504 46.5 wt % NYC 2.0 wt % TPO 1.5 wt %Irganox 1035 1.0 pph 3-Acryloxypropyl trimethoxysilane 0.8 pphPentaerythritol tetrakis(3-mercapto 0.032 pph propionate)where the oligomeric material was prepared as described above fromH12MDI, HEA, and PPG4000 using a molar ratio n:m:p=3.5:3.0:2.0, SR504 isethoxylated(4)nonylphenol acrylate (available from Sartomer), NVC isN-vinylcaprolactam (available from Aldrich), TPO (a photoinitiator) is(2,4,6-trimethylbenzoyl)-diphenyl phosphine oxide (available from BASF),Irganox 1035 (an antioxidant) is benzenepropanoic acid,3,5-bis(1,1-dimethylethyl)-4-hydroxythiodi-2,1-ethanediyl ester(available from BASF), 3-acryloxypropyl trimethoxysilane is an adhesionpromoter (available from Gelest), and pentaerythritoltetrakis(3-mercaptopropionate) (also known as tetrathiol, available fromAldrich) is a chain transfer agent. The concentration unit “pph” refersto an amount relative to a base composition that includes all monomers,oligomers, and photoinitiators. For example, a concentration of 1.0 pphfor Irganox 1035 corresponds to 1 g Irganox 1035 per 100 g combined ofoligomeric material, SR504, NVC, and TPO.

Secondary Coatings—Properties—Tensile Properties. The results of tensileproperty measurements prepared from the curable secondary compositionsare shown in Table 10.

TABLE 10 Tensile Properties of Secondary Coatings Tensile ElongationYield Young's Strength at yield Strength Modulus Composition (MPa) (%)(MPa) (MPa) KA 54.3 39.0 1528 KB 63.1 24.1 1703 KC 45.7 28.4 1242 KD61.8 32.5 1837 A 86.09 4.60 48.21 2049 SB 75.56 4.53 61.23 2532 SC 82.024.76 66.37 2653 SD 86.08 4.87 70.05 2776

The results show that secondary coatings prepared from compositions SB,SC, and SD exhibited higher Young's modulus, and higher yield strengththan the secondary coating prepared from comparative composition A. Thehigher values represent improvements that make secondary coatingsprepared for the curable coating compositions disclosed herein bettersuited for small diameter optical fibers. More specifically, the highervalues enable use of thinner secondary coatings on optical fiberswithout sacrificing performance. Thinner secondary coatings reduce theoverall diameter of the optical fiber and provide higher fiber counts incables of a given cross-sectional area.

The Young's modulus of secondary coatings prepared as cured productsfrom the curable secondary coating compositions disclosed herein isgreater than 2400 MPa, or greater than 2500 MPa, or greater than 2600MPa, or greater than 2700 MPa, or in the range from 2400 MPa to 3000MPa, or in the range from 2600 MPa to 2800 MPa.

The yield strength of secondary coatings prepared as cured products fromthe curable secondary coating compositions disclosed herein is greaterthan 55 MPa, or greater than 60 MPa, or greater than 65 MPa, or greaterthan 70 MPa, or in the range from 55 MPa to 75 MPa, or in the range from60 MPa to 70 MPa.

Secondary Coatings—Properties—Puncture Resistance. The punctureresistance of secondary coatings made from comparative curable secondarycoating composition A, a commercial curable secondary coatingcomposition (CPC6e) from a commercial vendor (DSM Desotech) having aproprietary composition, and curable secondary coating composition SDwas determined according to the method described above. Several fibersamples with each of the three secondary coatings were prepared. Eachfiber sample included a glass fiber with a diameter of 125 μm, a primarycoating formed from the reference primary coating composition listed inTable 9, and one of the three secondary coatings. Samples with varioussecondary coatings were prepared. The thicknesses of the primary coatingand secondary coating were adjusted to vary the cross-sectional area ofthe secondary coating as shown in FIG. 9 . The ratio of the thickness ofthe secondary coating to the thickness of the primary coating wasmaintained at about 0.8 for all samples.

Fiber samples with a range of thicknesses were prepared for each of thesecondary coatings to determine the dependence of puncture load on thethickness of the secondary coating. One strategy for achieving higherfiber count in cables is to reduce the thickness of the secondarycoating. As the thickness of the secondary coating is decreased,however, its performance diminishes and its protective function iscompromised. Puncture resistance is a measure of the protective functionof a secondary coating. A secondary coating with a high punctureresistance withstands greater impact without failing and provides betterprotection for the glass fiber.

The puncture load as a function of cross-sectional area for the threecoatings is shown in FIG. 9 . Cross-sectional area is selected as aparameter for reporting puncture load because an approximately linearcorrelation of puncture load with cross-sectional area of the secondarycoating was observed. Traces 92, 94, and 96 shows the approximate lineardependence of puncture load on cross-sectional area for the comparativesecondary coatings obtained by curing the comparative CPC6e secondarycoating composition, the comparative curable secondary coatingcomposition A, and curable secondary coating composition SD;respectively. The vertical dashed lines are provided as guides to theeye at cross-sectional areas of 10000 μm², 15000 μm², and 20000 μm² asindicated.

The CPC6e secondary coating depicted in Trace 92 corresponds to aconventional secondary coating known in the art. The comparativesecondary coating A depicted in Trace 94 shows an improvement inpuncture load for high cross-sectional areas. The improvement, however,diminishes as the cross-sectional area decreases. This indicates that asecondary coating obtained as a cured product from comparative curablesecondary coating composition A is unlikely to be suitable for lowdiameter, high fiber count applications. Trace 96, in contrast, shows asignificant increase in puncture load for the secondary coating obtainedas a cured product from curable secondary coating composition SD. At across-sectional area of 7000 μm², for example, the puncture load of thesecondary coating obtained from curable secondary coating composition SDis 50% or more greater than the puncture load of either of the other twosecondary coatings.

The puncture load of secondary coatings formed as cured products of thecurable secondary coating compositions disclosed herein at across-sectional area of 10000 μm² is greater than 36 g, or greater than40 g, or greater than 44 g, or greater than 48 g, or in the range from36 g to 52 g, or in the range from 40 g to 48 g. The puncture load ofsecondary coatings formed as cured products of the curable secondarycoating compositions disclosed herein at a cross-sectional area of 15000μm² is greater than 56 g, or greater than 60 g, or greater than 64 g, orgreater than 68 g, or in the range from 56 g to 72 g, or in the rangefrom 60 g to 68 g. The puncture load of secondary coatings formed ascured products of the curable secondary coating compositions disclosedherein at a cross-sectional area of 20000 μm² is greater than 68 g, orgreater than 72 g, or greater than 76 g, or greater than 80 g, or in therange from 68 g to 92 g, or in the range from 72 g to 88 g. Embodimentsinclude secondary coatings having any combination of the foregoingpuncture loads.

As used herein, normalized puncture load refers to the ratio of punctureload to cross-sectional area. The puncture load of secondary coatingsformed as cured products of the curable secondary coating compositionsdisclosed herein have a normalized puncture load greater than 3.2×10⁻³g/μm², or greater than 3.6×10⁻³ g/μm², or greater than 4.0×10⁻³ g/μm²,or greater than 4.4×10⁻³ g/μm², or greater than 4.8×10⁻³ g/μm², or inthe range from 3.2×10⁻³ g/μm² to 5.6×10⁻³ g/μm², or in the range from3.6×10⁻³ g/μm² to 5.2×10⁻³ g/μm², or in the range from 4.0×10⁻³ g/μm² to4.8×10⁻³ g/μm².

Design Examples—Coated Optical Fibers

Modeled Results. The experimental examples and principles disclosedherein indicate that by varying the mole numbers n, m, and p, it ispossible to control the relative amount of di-adduct compound in theoligomer as well as the properties of cured films formed from theprimary coating compositions over a wide range, including the rangesspecified herein for Young's modulus and in situ modulus. Similarly,variations in the type and concentration of different monomers in thesecondary composition leads to variations in the Young's modulus overthe range disclosed herein. Curing dose is another parameter that can beused to vary modulus of primary and secondary coatings formed from thecurable compositions disclosed herein.

To examine the effect of the thickness and modulus of the primary andsecondary coatings on transmission of a radial force to a glass fiber, aseries of modeled examples was considered. In the model, a radialexternal load P was applied to the surface of the secondary coating ofan optical fiber and the resulting load at the surface of the glassfiber was calculated. The glass fiber was modeled with a Young's modulusof 73.1 GPa (consistent with silica glass) and a diameter of 125 μm. ThePoisson ratios v_(p) and v_(s) of the primary and secondary coatingswere fixed at 0.48 and 0.33, respectively. A comparative sample Cl andsix samples M1-M6 in accordance with the present disclosure wereconsidered. The comparative sample included primary and secondarycoatings with thicknesses and moduli consistent with optical fibersknown in the art. Samples M1-M6 are examples with reduced thicknesses ofthe primary and secondary coatings. Parameters describing theconfigurations of the primary and secondary coatings are summarized inTable 11.

TABLE 11 Coating Properties of Modeled Optical Fibers Primary CoatingSecondary Coating In Situ Thick- Young's Thick- Modulus Diameter nessModulus Diameter ness Sample (MPa) (μm) (μm) (MPa) (μm) (μm) C1 0.20 19032.5 1600 242 26.0 M1 0.14 167 21.0 1900 200 16.5 M2 0.12 161 18.0 1900190 14.5 M3 0.10 155 15.0 2000 180 12.5 M4 0.09 150 12.5 2300 170 10.0M5 0.12 145 15.0 2200 170 12.5 M6 0.11 138 14.0 2200 160 11.0

Table 12 summarizes the load P1 at the outer surface of the glass fiberas a fraction of load P applied to the surface of the secondary coating.The ratio P1/P is referred to herein as the load transfer parameter andcorresponds to the fraction of external load P transmitted through theprimary and secondary coatings to the surface of the glass fiber. Theload P is a radial load and the load transfer parameter P1/P wascalculated from a model based on the equations below:

${\frac{P_{1}}{P} = \frac{4( {1 - v_{p}} )( {1 - v_{s}} )}{\{ {A + B} \}}}{where}{A = ( \frac{{E_{s}( {1 + v_{p}} )}( {1 - {2v_{p}}} )( {1 - ( {r_{4}/r_{5}} )^{2}} )( {1 - ( {r_{5}/r_{6}} )^{2}} )}{E_{p}( {1 + v_{s}} )} )}{and}{B = ( {( {1 - {2{v_{p}( {r_{4}/r_{5}} )}^{2}} + ( {r_{4}/r_{5}} )^{2}} )( {1 - {2{v_{s}( {r_{5}/r_{6}} )}^{2}} + ( {r_{5}/r_{6}} )^{2}} )} )}$In the equations, ν_(p) and ν_(s) are the Poisson's ratios of theprimary and secondary coatings, r₄ is the outer radius of the glassfiber, r₅ is the outer radius of the primary coating, r₆ is the outerradius of the secondary coating, E_(p) is the in situ modulus of theprimary coating, and E_(s) is the Young's modulus of the secondarycoating. The scaled load transfer parameter P1/P (scaled) in Table 12corresponds to the ratio P1/P for each sample relative to comparativesample C1.

TABLE 12 Load Transfer Parameter (P1/P) at Surface of Glass Fiber SampleP1/P P1/P (scaled) C1 0.0178 1.00 M1 0.0171 0.97 M2 0.0175 0.98 M30.0172 0.97 M4 0.0170 0.95 M5 0.0167 0.94 M6 0.0166 0.94

The modeled examples show that despite smaller coating thicknesses,optical fibers having primary and secondary coatings as described hereinexhibit a reduction in the force experienced by a glass fiber relativeto a comparative optical fiber having conventional primary and secondarycoatings with conventional thicknesses. The resulting reduction inoverall size of the optical fibers described herein enables higher fibercount in cables of a given size (or smaller cable diameters for a givenfiber count) without increasing the risk of damage to the glass fibercaused by external forces.

The scaled load transfer parameter P₁/P (scaled) of the secondarycoating is less than 0.99, or less than 0.97, or less than 0.95. Theload transfer parameter P₁/P of the secondary coating is less than0.0200, or less than 0.0180, or less than 0.0178, or less than 0.0176,or less than 0.0174, or less than 0.0172, or less than 0.0170, or lessthan 0.0168, or in the range from 0.0160-0.0180, or in the range from0.0162-0.0179, or in the range from 0.0164-0.0178, or in the range from0.0166-0.0177, or in the range from 0.0168-0.0176.

A first set of five modeled design examples Ex. 1 through Ex. 5 of thesingle mode optical fiber 100 as listed in Table 1 above with differentcoating designs and optical attributes are set forth in Table 13 below.All the exemplary optical fibers in Ex. 1-Ex. 5 set forth in Table 13have a small primary in situ modulus E_(p) (e.g., 0.2 MPa, 0.18 MPa, 0.1MPa, etc.) and a large secondary Young's modulus E_(s) (e.g., 2000 MPa,2250 MPa, 2300 MPa, 2500 MPa, 2775 MPa, etc.).

TABLE 13 Coating Design Examples of Mutimode Optical Fibers ParameterEx. 1 Ex. 2 Ex. 3 Ex. 4 Ex. 5 Diameter of glass fiber 2r_(4b) (μm) 8080.5 80 80 80.5 Primary in situ modulus E_(p) (MPa) 0.26 0.20 0.30 0.200.20 Primary coating diameter 2r₅ (μm) 120 120.5 110 130 130.5 Thicknessof primary coating 20 20 15 25 25 t_(p) or r₅-r_(4b) (μm) Primarycoating spring constant 1.04 0.805 1.60 0.64 0.64 χ_(p) (MPa) Secondarycoating in situ 1400 1800 1600 1500 1 modulus E_(s) (MPa) Secondarycoating diameter 2r₆ 165 157 155 155 165 (μm) Thickness of secondarycoating 22.5 18.5 22.5 12.5 17.5 r₆-r₅ (μm) Tertiary coating thicknessr₇-r₆ (μm) 0 4 5 5 0 Secondary + Tertiary coating 22.5 22.5 27.5 17.517.5 thickness t_(S) + t_(T) (μm) Ratio of Primary coating 0.89 0.890.55 1.43 1.43 thickness to (Secondary + Tertiary) coating thicknesst_(p)/(t_(S) + t_(T)) Secondary + Tertiary coating 40291 39913 4751732437 32028 cross sectional area (μm²) Coated fiber diameter 2r₇ 165 165165 165 165

Fabricating the Optical Fibers

The optical fibers described here can be made using the standardsmethods of making optical fiber. A core cane comprising the core and thetrench region can be made using processes such as OVD, VAD, MCVD andPCVD. In some embodiments, the first outer cladding layer and the secondouter cladding layer (e.g., titania-doped layer) can be put on the corecane in a single step to make the optical fiber preform. The first outercladding layer and the second outer cladding layer (e.g., titania-dopedlayer) can be deposited on the core cane in laydown as soot in a singlestep, with the silica precursor introduced to the laydown burner duringthe deposition of layers corresponding to the first outer claddinglayer, and silica and titania precursors introduced to the laydownburner during the deposition of layers corresponding to the second outercladding layer (e.g., titania-doped layer). Silica precursors includeSiCl₄ and OMCTS (octamethylcyclotetrasiloxane). Titania precursorsinclude TiCl₄ and titanium alkoxides (e.g. Ti(isopropoxide)₄). Theproduced cane-soot layer can then be moved to a onsolidation furnacewhere it can be first dehydrated using a dehydration agent and then thetemperature of the assembly can be increased to between 1350° C. to1500° C. to sinter the soot layer to a void free densified preforms. Insome embodiments, oxygen can be introduced during the sintering of thepreform process to have the titania oxidation state of 4+ that resultsin the titania-doped layer to have higher transparency. In someembodiments, the dehydration agent can be chosen from chlorine, thionylchlorine, silicon tetrachloride or combinations thereof. In someembodiments, the titania precursor can be titanium tetrachloride,titanium isopropoxide, or combination thereof. The formed sinteredoptical fiber can then be drawn into an optical fiber.

FIG. 10 is a schematic diagram of an example optical fiber drawingsystem (“drawing system”) 200 for drawing a glass preform 100P into theoptical fiber 100, according to some embodiments. The single modeoptical fiber 100 can be fabricated using the drawing system 200 andfiber drawing techniques known in the art.

The core and cladding layers of the glass preform can be produced in asingle-step process or multi-step process using chemical vapordeposition (CVD) methods which are well known in the art. A variety ofCVD processes are known and are suitable for producing the core andcladding layers used in the optical fibers of the present invention.They include outside vapor deposition process (OVD) process, vapor axialdeposition (VAD) process, modified CVD (MCVD), and plasma-enhanced CVD(PECVD).

As shown in FIG. 10 , the exemplary drawing system 200 can include adraw furnace (“furnace”) 102 for heating the glass preform 100P to theglass melt temperature. In an example, the fiber draw process is carriedout a glass melt temperature, which in an example is in the range from1800° C. to 1900° C. A preform holder 116 is used to hold the glasspreform 100P.

In some embodiments, the drawing system 200 also includes non-contactmeasurement sensors 104A and 104B for measuring the size of a drawn(bare) optical fiber 100G that exits the draw furnace 102 for size(diameter) control. A cooling station 106 can reside downstream of themeasurement sensors 104A and 104B and is configured to cool the bareoptical fiber 100G. A coating station 107 can reside downstream of thecooling station 106 and can be configured to deposit one or moreprotective coating materials 71 onto the bare optical fiber 100G to formthe protective coating 70 including the primary coating 72, thesecondary coating 74, and optionally the tertiary coating 76. Atensioner 220 can reside downstream of the coating station 107. Thetensioner 220 can have a surface 222 that pulls (draws) the coatedoptical fiber 100. A set of guide wheels 230 with respective surfaces232 resides downstream of the tensioner 220. The guide wheels 230 canserve to guide the coated optical fiber 100 to a fiber take-up spool(“spool”) 250 for storage.

In some embodiments, the close-up inset I1 of FIG. 10 shows across-sectional view of the glass preform 100P used to fabricate thesingle mode optical fiber 100. The glass preform 100P includes a preformcore 10P, and a preform cladding 50P comprising a preform inner claddingregion, a preform depressed-index cladding, a preform first outercladding, and a preform second outer cladding (not shown). In someembodiments, the preform core 10P can be a graded refractive index core.The preform 100P can be fabricated using known techniques, such as anoutside vapor deposition (OVD) process. The cross-sectional view of thecoated single mode optical fiber 100 can be referred to the descriptionsabove in connection with FIGS. 1 and 2 .

The disclosed single mode optical fibers are capable of being routedthrough extremely tight bend configurations or bending in a small radiusarc inside a fiber array unit that couples an array of fibers to arraysof lasers and photodiodes. The disclosed single mode optical fiberscomprise an outer cladding layer doped with titanium to increase thevalue of the fatigue constant, n_(d), and the reliability is furtherenhanced by a reduction in the out radius of the coated fiber to 85 μmor less. The disclosed single mode optical fibers fibers also have lowbend loss, which is achieved through the addition of a trench in theinner cladding. The dimensions of the core and the trench of the fiberscan be engineered to ensure that the fibers are single molded atwavelengths greater than or equal to 1260 nm for deployment lengths of 2meters or less. Advantages of the disclosed single mode optical fibersinclude: low bend loss, e.g., less than 1 dB/turn at a wavelength of1550 nm when wrapped around a mandrel having a diameter of 10 mm; lowshort-length cutoff wavelength, e.g., a fiber cutoff wavelength lessthan 1310 nm; G.652-compatible MFD, e.g., MFD≥8.2 μm at a wavelength of1310 nm; increased reliability for extremely tight bends achieved with areduced cladding diameter that includes an outer layer comprisingtitania-doped silica; and improved resistance to mechanical abrasion,which facilitates connectorization.

While various embodiments have been described herein, they have beenpresented by way of example only, and not limitation. It should beapparent that adaptations and modifications are intended to be withinthe meaning and range of equivalents of the disclosed embodiments, basedon the teaching and guidance presented herein. It therefore will beapparent to one skilled in the art that various changes in form anddetail can be made to the embodiments disclosed herein without departingfrom the spirit and scope of the present disclosure. The elements of theembodiments presented herein are not necessarily mutually exclusive, butmay be interchanged to meet various needs as would be appreciated by oneof skill in the art.

It is to be understood that the phraseology or terminology used hereinis for the purpose of description and not of limitation. The breadth andscope of the present disclosure should not be limited by any of theabove-described exemplary embodiments, but should be defined only inaccordance with the following claims and their equivalents.

What is claimed is:
 1. A single mode optical fiber, comprising: a coreregion, the core region having a radius r₁ in a range from 3 μm to 7 μmand a relative refractive index profile Δ₁ having a maximum relativerefractive index Δ_(1max) in the range from 0.25% to 0.50%; and acladding region surrounding and directly adjacent to the core region,the cladding region including a first outer cladding region and a secondouter cladding region surrounding and directly adjacent to the firstouter cladding region, the first outer cladding region having a radiusr_(4a), the second outer cladding region having a radius r_(4b) lessthan or equal to 45 μm, a relative refractive index Δ_(4b) greater than0.20%, and comprising silica based glass doped with titania.
 2. Thesingle mode optical fiber of claim 1, wherein the radius r₁ is in arange from 3.5 μm to 6.0 μm.
 3. The single mode optical fiber of claim1, wherein the relative refractive index profile Δ₁ is a graded-indexrelative refractive index profile.
 4. The single mode optical fiber ofclaim 1, wherein the relative refractive index profile Δ₁ is astep-index relative refractive index profile.
 5. The single mode opticalfiber of claim 1, wherein the maximum relative refractive index Δ_(1max)is in the range from 0.30% to 0.45%.
 6. The single mode optical fiber ofclaim 1, wherein the cladding region includes an inner cladding regionsurrounding and directly adjacent to the core region, the inner claddingregion having a radius r₂, a thickness (r₂-r₁) in a range from 2 μm to 8μm and a relative refractive index Δ₂ in a range from −0.10% to 0.10%.7. The single mode optical fiber of claim 6, wherein the cladding regionfurther comprises a depressed-index cladding region surrounding anddirectly adjacent to the inner cladding region, the depressed-indexcladding region having a radius r₃, a thickness (r₃−r₂) in a range from3 μm to 10 μm, and a relative refractive index Δ₃ in a range from −0.70%to −0.20%.
 8. The single mode optical fiber of claim 7, wherein thethickness (r₃−r₂) in a range from 4 μm to 8 μm.
 9. The single modeoptical fiber of claim 7, wherein the depressed-index cladding regionhas a has a trench volume V₃ in a range from 30% Δ-μm² to 80%Δ-μm². 10.The single mode optical fiber of claim 7, wherein the first outercladding region surrounds and is directly adjacent to thedepressed-index cladding region.
 11. The single mode optical fiber ofclaim 1, wherein the first outer cladding region has a relativerefractive index Δ_(4a) that is in the range from −0.10% to 0.10%. 12.The single mode optical fiber of claim 1, wherein the second outercladding region has a titania concentration in a range from 5 wt % to 20wt %.
 13. The single mode optical fiber of claim 1, wherein the radiusr_(4b) is less than or equal to 40 μm.
 14. The single mode optical fiberof claim 1, wherein the second outer cladding region has a thickness(r_(4b)−r_(4a)) in a range from 2 μm to 30 μm.
 15. The single modeoptical fiber of claim 1, further comprising: a primary coatingsurrounding and directly adjacent to the second outer cladding region,the primary coating having a radius r₅ less than or equal to 65 μm, aspring constant χ_(p) less than 1.2 MPa, an in situ modulus in the rangefrom 0.05 MPa to 0.30 MPa, and a thickness (r₅−r₄) less than 30 μm. 16.The single mode optical fiber of claim 15, wherein the spring constantχ_(p) is less than 0.8 MPa.
 17. The single mode optical fiber of claim15, wherein the thickness (r₅−r₄) is less than 20 μm.
 18. The singlemode optical fiber of claim 15, wherein the primary coating is a curedproduct of a coating composition comprising: a radiation-curablemonomer; an adhesion promoter, the adhesion promoter comprising analkoxysilane compound or a mercapto-functional silane compound; and anoligomer, the oligomer comprising: a polyether urethane acrylatecompound having the molecular formula:

wherein R₁, R₂ and R₃ are independently selected from linear alkylenegroups, branched alkylene groups, or cyclic alkylene groups; y is 1, 2,3, or 4; and x is between 40 and 100; and a di-adduct compound havingthe molecular formula:

wherein the di-adduct compound is present in an amount of at least 1.0wt % in the oligomer.
 19. The single mode optical fiber of claim 18,wherein the oligomer is the cured product of a reaction between: adiisocyanate compound; a hydroxy (meth)acrylate compound; and a polyolcompound, said polyol compound having unsaturation less than 0.1 meq/g;wherein said diisocyanate compound, said hydroxy (meth)acrylate compoundand said polyol compound are reacted in molar ratios n:m:p,respectively, wherein n is in the range from 3.0 to 5.0, m is within±15% of 2n−4, and p is
 2. 20. The single mode optical fiber of claim 15,further comprising: a secondary coating surrounding and directlyadjacent to the primary coating, the secondary coating having a radiusr₆ less than or equal to 85 μm, a Young's modulus greater than 1600 MPaand a thickness (r₆−r₅) less than 30 μm.
 21. The single mode opticalfiber of claim 20, wherein the radius r₆ is less than or equal to 80 μm.22. The single mode optical fiber of claim 20, wherein the thickness(r₆−r₅) is less than 20 μm.
 23. The single mode optical fiber of claim20, wherein the secondary coating is the cured product of a compositioncomprising: an alkoxylated bisphenol-A diacrylate monomer in an amountgreater than 55 wt %, the alkoxylated bisphenol-A diacrylate monomerhaving a degree of alkoxylation in the range from 2 to 16; and atriacrylate monomer in an amount in the range from 2.0 wt % to 25 wt %,the triacrylate monomer comprising an alkoxylated trimethylolpropanetriacrylate monomer having a degree of alkoxylation in the range from 2to 16 or a tris[(acryloyloxy)alkyl] isocyanurate monomer.
 24. The singlemode optical fiber of claim 20, wherein a ratio R_(ps) of the thickness(r₅−r₄) of the primary coating to the thickness (r₆−r₅) of the secondarycoating is in a range from 0.90 to 1.50.
 25. The single mode opticalfiber of claim 1, wherein the single mode optical fiber has a fibercutoff wavelength χ_(CF) less than 1310 nm.
 26. The single mode opticalfiber of claim 1, wherein the single mode optical fiber has a mode fielddiameter (MFD) greater than 8.2 μm at 1310 nm.
 27. The single modeoptical fiber of claim 1, wherein the single mode optical fiber has abend loss at 1550 nm, as determined by a mandrel wrap test using amandrel with a diameter of 10 mm, less than 0.5 dB/turn.